A216429 Numbers k such that the k-th Fibonacci number can be written in the form a^2 + 7*b^2.

0, 1, 2, 6, 12, 13, 17, 19, 24, 29, 31, 34, 38, 47, 83, 102, 109, 127, 131, 193, 271, 307, 323, 397, 419, 431, 433, 449, 461, 467, 479, 493, 509, 614, 643, 646, 653, 673, 899, 1069, 1091, 1346

Offset

1,3

Comments

These Fibonacci numbers F(k) have no prime factors congruent to 3, 5 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..42.

Blair Kelly, Factorizations of Fibonacci and Lucas numbers

Crossrefs

Cf. A020670.

Sequence in context: A062723 A152667 A145892 * A250178 A154712 A079849

Adjacent sequences: A216426 A216427 A216428 * A216430 A216431 A216432

Keyword

nonn

Author

V. Raman, Sep 08 2012

Status

approved