

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; sequence smallest such new prime.


2



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
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OFFSET

3,1


COMMENTS

Carmichael showed that the sequence is welldefined.
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 A061488=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

A061488(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. 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



