A216433 Numbers k such that the k-th Lucas number can be written in the form a^2 + 7*b^2.

1, 3, 4, 5, 7, 16, 17, 19, 21, 32, 35, 37, 49, 51, 53, 64, 71, 76, 80, 85, 97, 101, 113, 119, 128, 133, 147, 148, 160, 181, 199, 211, 212, 224, 229, 241, 245, 259, 263, 293, 307, 311, 320, 323, 343, 352, 353, 355, 357, 371, 401, 416, 421, 464, 497, 503, 524, 544, 577, 593, 595

Offset

1,2

Comments

These Lucas numbers L(k) 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

V. Raman, Table of n, a(n) for n = 1..82

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Crossrefs

Sequence in context: A060728 A330712 A295988 * A101761 A035359 A365577

Adjacent sequences: A216430 A216431 A216432 * A216434 A216435 A216436

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved