A128288 a(n) = A023163(n)/3 for n > 1.

3, 13, 37, 43, 53, 67, 83, 107, 157, 163, 173, 197, 227, 277, 283, 293, 307, 317, 347, 373, 397, 443, 467, 523, 547, 557, 563, 587, 613, 643, 653, 677, 683, 733, 757, 773, 787, 797, 827, 853, 877, 883, 907, 947, 997, 1013, 1093, 1117, 1123, 1163, 1187, 1213

Offset

2,1

Comments

3 divides A023163(n) for n > 1. A023163(n) are the numbers n such that Fibonacci(n) == -2 (mod n). Almost all terms of {a(n)} are prime that belong to A003631 = {2, 3, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97} (primes congruent to {2, 3} mod 5) that are also the primes p that divide Fibonacci(p+1). The first composite term is a(74) = 1853 = 17*109. The second composite term is 9701 = 89*109. The third composite term is 10877 = 73*149 belong to A069107(n) Composite n such that n divides F(n+1) where F(k) are the Fibonacci numbers. Composite terms in {a(n)} are listed in A128289 = {1853, 9701, 10877, 17261, ...}.

Links

Table of n, a(n) for n=2..53.

Formula

a(n) = A023163(n)/3 for n > 1.

Example

A023163 begins {1, 9, 39, 111, 129, 159, 201, 249, 321, 471, 489, 519, ...}.
Thus a(2) = A023163(2)/3 = 9/3 = 3, a(3) = A023163(3)/3 = 39/3 = 13.

Crossrefs

Cf. A002708, A023172, A023173, A023162, A023163 (numbers k such that Fibonacci(k) == -2 (mod k)).

Cf. A003631, A069107, A128289 (composite terms in A128288).

Sequence in context: A146049 A061483 A340410 * A113115 A107136 A153009

Adjacent sequences: A128285 A128286 A128287 * A128289 A128290 A128291

Keyword

nonn

Author

Alexander Adamchuk, Feb 24 2007

Status

approved