A135953 - OEIS

A135953

(Nonprime Fibonacci numbers with prime indices) which have exactly 2 prime factors.

4181, 1346269, 165580141, 53316291173, 956722026041, 2504730781961, 308061521170129, 806515533049393, 14472334024676221, 1779979416004714189, 573147844013817084101, 10284720757613717413913, 26925748508234281076009

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OFFSET

1,1

COMMENTS

Conjecture: All numbers in this sequence are products of two sums of two squares, e.g. 4181 = 37*113 = (1^2+6^2)(7^2+8^2), 1346269=557*2417 = (14^2+19^2)(4^2+49^2).

LINKS

Table of n, a(n) for n=1..13.

MATHEMATICA

k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], c = Length[FactorInteger[Fibonacci[Prime[n]]]]; If[c == 2, AppendTo[k, Fibonacci[Prime[n]]]]], {n, 1, 50}]; k

Select[Fibonacci[Prime[Range[30]]], PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 18 2012 *)

CROSSREFS

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852, A135954, A135955, A135956, A135957.

Sequence in context: A048593 A358555 A050937 * A290846 A236805 A202530

Adjacent sequences: A135950 A135951 A135952 * A135954 A135955 A135956

KEYWORD

nonn

AUTHOR

Artur Jasinski, Dec 08 2007

STATUS

approved