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%I #30 Dec 21 2022 04:37:14
%S 2,3,5,13,7,17,11,89,233,29,61,47,1597,19,37,41,421,199,28657,23,3001,
%T 521,53,281,514229,31,557,2207,19801,3571,141961,107,73,9349,135721,
%U 2161,2789,211,433494437,43,109441,139,2971215073,1103,97,101,6376021
%N 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.
%C Carmichael showed that the sequence is well defined.
%C Same as A001578 without the "1" terms.
%C 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
%H T. D. Noe, <a href="/A061488/b061488.txt">Table of n, a(n) for n=3..998</a>
%H Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibmaths.html">Mathematics of the Fibonacci Series</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha108.htm">Factorizations of many number sequences</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha109.htm">Factorizations of many number sequences</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha110.htm">Factorizations of many number sequences</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha111.htm">Factorizations of many number sequences</a>
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha112.htm">Factorizations of many number sequences</a>
%F a(n) = A001578(n+2) from n=11 on. - _M. F. Hasler_, Oct 21 2012
%t 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 *)
%Y Cf. A000045, A061446.
%K nonn,easy,nice
%O 3,1
%A _N. J. A. Sloane_, Nov 08 2001
%E More terms from _Vladeta Jovovic_ and _Lior Manor_ Nov 09 2001
%E Corrected by _T. D. Noe_, Feb 10 2007
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