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

Author

N. J. A. Sloane, Nov 08 2001

Keywords

• nonn
• easy
• nice

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

Crossrefs

Cf. A000045, A061446.

Programs

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 *)

Formula

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

Extensions

More terms from Vladeta Jovovic and Lior Manor, Nov 09 2001

Corrected by T. D. Noe, Feb 10 2007