A216526 Prime numbers n such that (10^n-1)/9 can be written in the form a^2+7*b^2.

2, 7, 13, 19, 23, 37, 47, 53, 59, 71, 73, 83, 101, 103, 127, 149, 151, 191, 211, 317

Offset

1,1

Comments

These repunit numbers of the form (10^n-1)/9 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..20.

Samuel S. Wagstaff, Jr. The Cunningham Project

Mathematica

Select[Prime[Range[70]], Length[Solve[a^2+7b^2==(10^#-1)/9, {a, b}, Integers]] > 0&] (* Harvey P. Dale, Aug 19 2015 *)

Crossrefs

Sequence in context: A156007 A067774 A063637 * A020623 A109346 A140550

Adjacent sequences: A216523 A216524 A216525 * A216527 A216528 A216529

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved