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A235383 Fibonacci numbers that are the product of other Fibonacci numbers. 5
8, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence and A229037 and A235265 are winners in the contest held at the 2014 AMS/MAA Joint Mathematics Meetings. - T. D. Noe, Jan 20 2014

Carmichael's theorem implies that 8 and 144 are the only terms of this sequence.

First two terms of A061899, A111687, A172150, A212703, and A231851. - Omar E. Pol, Jan 21 2014

Saha and Karthik conjectured (without reference to Carmichael's theorem) that the only positive integers k for which A001175(k^2) = A001175(k) are 6 and 12. (A000045(6) = 8 and A000045(12) = 144.) - L. Edson Jeffery, Feb 13 2014

Y. Bugeaud, M. Mignotte, and S. Siksek proved that 8 and 144 are the only nontrivial perfect power Fibonacci numbers. - Robert C. Lyons, Dec 23, 2015

LINKS

Table of n, a(n) for n=1..2.

Yann Bugeaud, Maurice Mignotte, and Samir Siksek, Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers, Annals of Mathematics, 163 (2006), pp. 969-1018.

Arpan Saha and Karthik C S, A few equivalences of Wall-Sun-Sun prime conjecture, arXiv:1102.1636 [math.NT], 2011.

Wikipedia, Carmichael's theorem.

EXAMPLE

The Fibonacci number 8 is in the sequence because 8=2*2*2, and 2 is a Fibonacci number that is not equal to 8. The Fibonacci number 144 is in the sequence because 144=3*3*2*2*2*2, and both 2 and 3 are Fibonacci numbers that are not equal to 144.

CROSSREFS

Cf. A000045, A061899, A065108, A227875.

Sequence in context: A180357 A112464 A227875 * A275034 A275139 A241229

Adjacent sequences:  A235380 A235381 A235382 * A235384 A235385 A235386

KEYWORD

nonn,bref,fini,full,nice

AUTHOR

Robert C. Lyons, Jan 08 2014

STATUS

approved

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Last modified February 23 18:54 EST 2018. Contains 299586 sequences. (Running on oeis4.)