A216524 Prime numbers n such that (2^n+1)/3 can be written in the form a^2+7*b^2.

5, 7, 11, 13, 17, 19, 23, 31, 43, 53, 61, 67, 79, 89, 101, 127, 139, 167, 179, 191, 199, 211, 223, 227, 269, 313, 317, 347, 389, 431, 433, 457, 503, 593, 601, 613, 619, 673, 701, 739, 797, 827, 839, 907, 967

Offset

1,1

Comments

These numbers of the form (2^n+1)/3 have no prime factors congruent to 3 (mod 7) or 5 (mod 7) or 6 (mod 7) to an odd power. Also the power of 2 is not 1.

Links

Table of n, a(n) for n=1..45.

Samuel S. Wagstaff, Jr. The Cunningham Project

Mathematica

Select[Prime[Range[170]], FindInstance[a^2+7b^2==(2^#+1)/3, {a, b}, Integers] != {}&] (* Harvey P. Dale, Sep 04 2020 *)

Crossrefs

Sequence in context: A101635 A118941 A096547 * A128824 A098420 A346676

Adjacent sequences: A216521 A216522 A216523 * A216525 A216526 A216527

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved