A122094 -id:A122094 - cp's OEIS frontend

A219341 Least prime k such that k*2^n + 1 divides 2^k - 1, or 0 if no such prime exists.

2, 3, 0, 11, 397, 839, 1459, 2081, 7297, 53849, 3499, 70589, 792277, 20399, 11173873, 929057, 232591, 6782759, 5834299, 26812151, 40269673, 88529891, 368454343, 616767917, 1167319801, 709939943, 38151887029, 38617336361, 23280518791, 168046587719, 882701485339

Offset: 0

Arkadiusz Wesolowski, Nov 18 2012

nonn

If a(n) > 0, then a(n)*2^n + 1 is in A122094.

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 232591
Eric Weisstein's World of Mathematics, Mersenne Number

Cf. A001348, A002144.

lst = {}; Do[k = 2; If[n == 2, AppendTo[lst, 0], While[True, If[PrimeQ[k], f = k*2^n + 1; If[PrimeQ[f] && PowerMod[2, k, f] == 1, AppendTo[lst, k]; Break[]]]; k++]], {n, 0, 13}]; lst

a(26)-a(30) from Jason Yuen, May 24 2024

A256172 Primes of the form 6p + 1 with p prime that are also of the form x^2 + 27y^2 and congruent to 7 mod 24.

Original entry on oeis.org

31, 223, 439, 1399, 2383, 2767, 3343, 3463, 3607, 4567, 6079, 7927, 8167, 8287, 8719, 10159, 10663, 11959, 14503, 15559, 15727, 17383, 18223, 19087, 20743, 21487, 21559, 24007, 25639, 26647, 27103, 27583, 28807, 28879, 29167, 29599, 31183, 32359, 33343

Offset: 1

Arkadiusz Wesolowski, Jun 01 2015

nonn

a(n) divides 2^m - 1, where m = (a(n) - 7)/6 + 1.

Subsequence of A122094.

Cf. A014752, A051644, A107006.

A014752 INTERSECT A051644 INTERSECT A107006.

cp's OEIS Frontend

A219341 Least prime k such that k*2^n + 1 divides 2^k - 1, or 0 if no such prime exists.

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A256172 Primes of the form 6p + 1 with p prime that are also of the form x^2 + 27y^2 and congruent to 7 mod 24.

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cp's OEIS Frontend

A219341 Least prime k such that k*2^n + 1 divides 2^k - 1, or 0 if no such prime exists.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A256172 Primes of the form 6*p + 1 with p prime that are also of the form x^2 + 27*y^2 and congruent to 7 mod 24.

Views

Author

Keywords

Comments

Crossrefs

Formula

A256172 Primes of the form 6p + 1 with p prime that are also of the form x^2 + 27y^2 and congruent to 7 mod 24.