A177745 Semiprimes k that divide Fibonacci(k+1).

323, 377, 3827, 5777, 10877, 11663, 18407, 19043, 23407, 25877, 27323, 34943, 39203, 51983, 53663, 60377, 75077, 86063, 94667, 100127, 113573, 121103, 121393, 161027, 162133, 182513, 195227, 200147, 231703, 240239, 250277, 294527, 306287, 345913, 381923, 429263, 430127, 454607, 500207, 507527, 548627, 569087, 600767, 635627, 636707, 685583, 697883, 736163, 753377, 775207, 828827, 851927, 948433, 983903

Offset

1,1

Comments

Data from T. D. Noe.

Links

Table of n, a(n) for n=1..54.

Formula

{k: k is in A001358 and k|A000045(k+1)}.

Example

a(1) = 323 = 17 * 19 because it is semiprime (product of two prime A000040), and 323 divides F(324) = 23041483585524168262220906489642018075101617466780496790573690289968, with dividend 2^4 * 3^5 * 53 * 107 * 109 * 2269 * 3079 * 4373 * 5779 * 19441 * 11128427 * 62650261 * 1828620361 * 6782976947987.

Mathematica

With[{semis=Select[Range[1000000], PrimeOmega[#]==2&]}, Select[semis, Divisible[Fibonacci[#+1], #]&]] (* Harvey P. Dale, Aug 20 2012 *)

Crossrefs

Cf. A177086, A000045, A001358, A069106, A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).

Sequence in context: A069107 A094412 A182504 * A065822 A279072 A158306

Adjacent sequences: A177742 A177743 A177744 * A177746 A177747 A177748

Keyword

nonn,easy

Author

Jonathan Vos Post, Dec 12 2010

Status

approved