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==Countings: Sequences per type==
 
==Countings: Sequences per type==
−
Sequences (per base, k-value or individual number) with own page in this Wiki:
+
Sequences (per base, {{Vk}}-value or individual number) with own page in this Wiki:
 
{| class="wikitable"
 
{| class="wikitable"
 
!Sequence!!Type!!counting
 
!Sequence!!Type!!counting
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| [[:Category:Mersenne prime|Mersenne primes]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Mersenne prime|pages|R}}-2}}}}
 
| [[:Category:Mersenne prime|Mersenne primes]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Mersenne prime|pages|R}}-2}}}}
 
|-
 
|-
−
| [[:Category:Riesel prime|Riesel primes {{Kbn|k|2|n}}]] || k-value || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Riesel prime|pages|R}}-2}}}}
+
| [[:Category:Riesel prime|Riesel primes {{Kbn|k|2|n}}]] || {{Vk}}-value || style="text-align:right;"|{{Num|{{PAGESINCATEGORY:Riesel 2|pages|R}}}}
 
|-
 
|-
−
| [[:Category:Gen. Riesel prime|Gen. Riesel primes {{Kbn|k|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Riesel prime|subcats|R}}}}}}
+
| [[:Category:Riesel prime|Riesel primes {{Kbn|k|b|n}}]], {{Vb}}>2 || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Riesel prime|subcats|R}}-3}}}}
 
|-
 
|-
−
| [[:Category:Proth prime|Proth primes {{Kbn|+|k|2|n}}]] || k-value || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Proth prime|pages|R}}-3}}}}
+
| [[:Category:Proth 2|Proth primes {{Kbn|+|k|2|n}}]] || {{Vk}}-value || style="text-align:right;"|{{Num|{{PAGESINCATEGORY:Proth 2|pages|R}}}}
 
|-
 
|-
−
| [[:Category:Gen. Proth prime|Gen. Proth primes {{Kbn|+|k|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Proth prime|subcats|R}}}}}}
+
| [[:Category:Proth prime|Proth primes {{Kbn|+|k|b|n}}]], {{Vb}}>2 || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Proth prime|subcats|R}}-1}}}}
 
|-
 
|-
−
| [[:Category:Carol-Kynea prime|Carol-Kynea primes (b<sup>n</sup>±1)<sup>2</sup>-2]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Carol-Kynea prime|pages|R}}-4}}}}
+
| [[:Category:Carol-Kynea prime|Carol-Kynea primes ({{Vb}}<sup>{{Vn}}</sup>±1)<sup>2</sup>-2]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Carol-Kynea prime|pages|R}}-4}}}}
 
|-
 
|-
 
| [[:Category:Williams prime MM|Williams primes {{Kbn|(b-1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Williams prime MM|pages|R}}-3}}}}
 
| [[:Category:Williams prime MM|Williams primes {{Kbn|(b-1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Williams prime MM|pages|R}}-3}}}}
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| [[:Category:Williams prime PP|Williams primes {{Kbn|+|(b+1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Williams prime PP|pages|R}}-3}}}}
 
| [[:Category:Williams prime PP|Williams primes {{Kbn|+|(b+1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Williams prime PP|pages|R}}-3}}}}
 
|-
 
|-
−
| [[:Category:Leyland prime P|Leyland numbers x<sup>y</sup>+y<sup>x</sup>]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Leyland prime P|pages|R}}-2}}}}
+
| [[:Category:Leyland prime P|Leyland numbers {{V|x}}<sup>{{V|y}}</sup>+{{V|y}}<sup>{{V|x}}</sup>]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Leyland prime P|pages|R}}-2}}}}
 
|-
 
|-
−
| [[:Category:Leyland prime M|Leyland numbers x<sup>y</sup>-y<sup>x</sup>]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Leyland prime M|pages|R}}}}}}
+
| [[:Category:Leyland prime M|Leyland numbers {{V|x}}<sup>{{V|y}}</sup>-{{V|y}}<sup>{{V|x}}</sup>]] || number || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Leyland prime M|pages|R}}}}}}
 
|-
 
|-
−
| [[:Category:Gen. Woodall prime|Gen. Woodall primes {{Kbn|n|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Woodall prime|pages|R}}-2}}}}
+
| [[:Category:Woodall prime|Woodall primes {{Kbn|n|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Woodall prime|pages|R}}-2}}}}
 
|-
 
|-
−
| [[:Category:Gen. Woodall prime M|Near Gen. Woodall primes {{Kbn|(n-1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Woodall prime M|pages|R}}-1}}}}
+
| [[:Category:Woodall prime M|Near Woodall primes {{Kbn|(n-1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Woodall prime M|pages|R}}-1}}}}
 
|-
 
|-
−
| [[:Category:Gen. Woodall prime P|Near Gen. Woodall primes {{Kbn|(n+1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Woodall prime P|pages|R}}-1}}}}
+
| [[:Category:Woodall prime P|Near Woodall primes {{Kbn|(n+1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Woodall prime P|pages|R}}-1}}}}
 
|-
 
|-
−
| [[:Category:Gen. Cullen prime|Gen. Cullen primes {{Kbn|+|n|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Gen. Cullen prime|pages|R}}-2}}}}
+
| [[:Category:Cullen prime|Cullen primes {{Kbn|+|n|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Cullen prime|pages|R}}-2}}}}
 +
|-
 +
| [[:Category:Cullen prime M|Near Cullen primes {{Kbn|+|(n-1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Cullen prime M|pages|R}}-0}}}}
 +
|-
 +
| [[:Category:Cullen prime P|Near Cullen primes {{Kbn|+|(n+1)|b|n}}]] || base || style="text-align:right;"|{{Num|{{#expr:{{PAGESINCATEGORY:Cullen prime P|pages|R}}-0}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 2|Fermat numbers {{V|F}}(2)]] || number || style="text-align:right;"|{{PAGESINCATEGORY:Generalized Fermat number 2 1 Nums|pages|R}}
 +
|-
 +
| [[:Category:Generalized Fermat number 2|GF Divisors (2)]] || number || style="text-align:right;"|{{PAGESINCATEGORY:Generalized Fermat number 2 1 Divs|pages|R}}
 +
|-
 +
| [[:Category:Generalized Fermat number 3|Gen.Fermat numbers {{V|xGF}}(3)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 3 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 3 2 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 3|GF Divisors (3)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 3 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 3 2 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 4|Gen.Fermat numbers {{V|xGF}}(4)]] || number || style="text-align:right;"|{{PAGESINCATEGORY:Generalized Fermat number 4 3 Nums|pages|R}}
 +
|-
 +
| [[:Category:Generalized Fermat number 4|GF Divisors (4)]] || number || style="text-align:right;"|{{PAGESINCATEGORY:Generalized Fermat number 4 3 Divs|pages|R}}
 +
|-
 +
| [[:Category:Generalized Fermat number 5|Gen.Fermat numbers {{V|xGF}}(5)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 5 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 2 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 3 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 4 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 5|GF Divisors (5)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 5 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 2 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 3 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 5 4 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 6|Gen.Fermat numbers {{V|xGF}}(6)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 6 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 6 5 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 6|GF Divisors (6)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 6 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 6 5 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 7|Gen.Fermat numbers {{V|xGF}}(7)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 7 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 2 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 3 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 4 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 5 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 6 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 7|GF Divisors (7)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 7 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 2 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 3 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 4 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 5 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 7 6 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 8|Gen.Fermat numbers {{V|xGF}}(8)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 8 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 3 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 5 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 7 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 8|GF Divisors (8)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 8 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 3 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 5 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 8 7 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 9|Gen.Fermat numbers {{V|xGF}}(9)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 9 2 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 5 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 7 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 8 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 9|GF Divisors (9)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 9 2 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 5 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 7 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 9 8 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 10|Gen.Fermat numbers {{V|xGF}}(10)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 10 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 3 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 7 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 9 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 10|GF Divisors (10)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 10 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 3 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 7 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 10 9 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 11|Gen.Fermat numbers {{V|xGF}}(11)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 11 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 2 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 3 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 4 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 5 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 6 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 7 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 8 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 9 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 10 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 11|GF Divisors (11)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 11 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 2 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 3 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 4 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 5 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 6 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 7 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 8 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 9 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 11 10 Divs|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 12|Gen.Fermat numbers {{V|xGF}}(12)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 12 1 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 12 5 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 12 7 Nums|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 12 11 Nums|pages|R}}}}
 +
|-
 +
| [[:Category:Generalized Fermat number 12|GF Divisors (12)]] || number || style="text-align:right;"|{{#expr:{{PAGESINCATEGORY:Generalized Fermat number 12 1 Divs|pages|R}}+{{PAGESINCATEGORY:Generalized Fermat number 12 5 Divs|pages|R}}+{{#dpl:category=Generalized Fermat number 12 7 Divs|resultsheader=%PAGES%|mode=userformat}}+{{#dpl:category=Generalized Fermat number 12 11 Divs|resultsheader=%PAGES%|mode=userformat}}}}
 +
|-
 +
| [[:Category:GF Divisors|all GF Divisors]] || number || style="text-align:right;"|{{#dpl:category=GF Divisors|resultsheader=%PAGES%|mode=userformat}}
 
|}
 
|}
 
{{Navbox NumberClasses}}
 
{{Navbox NumberClasses}}
 
[[Category:System]]
 
[[Category:System]]

Revision as of 07:49, 24 September 2021

Countings: Sequences per type

Sequences (per base, k-value or individual number) with own page in this Wiki:

Sequence Type counting
Mersenne primes number 51
Riesel primes k•2n-1 k-value 3,837
Riesel primes k•bn-1, b>2 base 12
Proth primes k•2n+1 k-value 154
Proth primes k•bn+1, b>2 base 6
Carol-Kynea primes (bn±1)2-2 base 382
Williams primes (b-1)•bn-1 base 169
Williams primes (b-1)•bn+1 base 154
Williams primes (b+1)•bn-1 base 87
Williams primes (b+1)•bn+1 base 82
Leyland numbers xy+yx number 1,814
Leyland numbers xy-yx number 1
Woodall primes n•bn-1 base 776
Near Woodall primes (n-1)•bn-1 base 4
Near Woodall primes (n+1)•bn-1 base 3
Cullen primes n•bn+1 base 139
Near Cullen primes (n-1)•bn+1 base 1
Near Cullen primes (n+1)•bn+1 base 1
Fermat numbers F(2) number 150
GF Divisors (2) number 185
Gen.Fermat numbers xGF(3) number 21
GF Divisors (3) number 202
Gen.Fermat numbers xGF(4) number 4
GF Divisors (4) number 62
Gen.Fermat numbers xGF(5) number 15
GF Divisors (5) number 363
Gen.Fermat numbers xGF(6) number 11
GF Divisors (6) number 148
Gen.Fermat numbers xGF(7) number 26
GF Divisors (7) number 441
Gen.Fermat numbers xGF(8) number 23
GF Divisors (8) number 365
Gen.Fermat numbers xGF(9) number 17
GF Divisors (9) number 348
Gen.Fermat numbers xGF(10) number 18
GF Divisors (10) number 276
Gen.Fermat numbers xGF(11) number 45
GF Divisors (11) number 744
Gen.Fermat numbers xGF(12) number 14
GF Divisors (12) number 310
all GF Divisors number 1165
Number classes
General numbers
Special numbers
Prime numbers
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