A061488 Factorize the Fibonacci numbers in order, skipping F(0)-F(2), F(6)=8 and F(12)=144; at each step at least one new prime will occur; append to the sequence the smallest such new prime.

2, 3, 5, 13, 7, 17, 11, 89, 233, 29, 61, 47, 1597, 19, 37, 41, 421, 199, 28657, 23, 3001, 521, 53, 281, 514229, 31, 557, 2207, 19801, 3571, 141961, 107, 73, 9349, 135721, 2161, 2789, 211, 433494437, 43, 109441, 139, 2971215073, 1103, 97, 101, 6376021

Offset

3,1

Comments

Carmichael showed that the sequence is well defined.

Same as A001578 without the "1" terms.

Given the definition, in particular omission of F(6) and F(12), setting offset=1 would be more adequate; offset=5 (= number of omitted terms) would give A001578 for n > 12 on. - M. F. Hasler, Oct 21 2012

Links

T. D. Noe, Table of n, a(n) for n=3..998

Ron Knott, Mathematics of the Fibonacci Series

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

Formula

a(n) = A001578(n+2) from n=11 on. - M. F. Hasler, Oct 21 2012

Mathematica

f[n_] := Block[{p = First /@ FactorInteger[ Fibonacci[ n]]}, k = 1; lmt = 1 + Length@ p; While[k < lmt && MemberQ[lst, p[[k]]], k++]; If[k < lmt, AppendTo[lst, p[[k]]]]]; lst = {}; Do[ f[n], {n, 3, 51}]; lst (* Robert G. Wilson v, Oct 23 2012 *)

Crossrefs

Cf. A000045, A061446.

Sequence in context: A193064 A133832 A328997 * A236394 A111239 A264745

Adjacent sequences: A061485 A061486 A061487 * A061489 A061490 A061491

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Nov 08 2001

Extensions

More terms from Vladeta Jovovic and Lior Manor Nov 09 2001

Corrected by T. D. Noe, Feb 10 2007

Status

approved