A115037 A number n is included if largest prime (or 1 if no prime divides) dividing the n-th Fibonacci number is itself a Fibonacci number.

1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 17, 23, 29, 43, 46, 47, 58, 69, 83, 86, 129, 131, 137, 141, 166, 262, 274, 332, 359, 411, 431, 433, 449, 509, 569, 571, 718, 862, 866, 898, 1018, 1138, 1142, 1293, 1347, 1436

Offset

1,2

Comments

A001605 is a subsequence. 2036 and 2276 are also terms. - Chai Wah Wu, May 19 2020

Links

Table of n, a(n) for n=1..46.

Example

The 12th Fibonacci number is 144. The largest prime dividing 144 is 3 and 3 is the 4th Fibonacci number. So 12 is in the sequence.

Prog

(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(n) = my(f=fibonacci(n)); (f==1) || isfib(vecmax(factor(f)[, 1])); \\ Michel Marcus, Sep 06 2019

Crossrefs

Cf. A000045, A001605, A060385.

Sequence in context: A358673 A032976 A174219 * A280536 A090563 A045745

Adjacent sequences: A115034 A115035 A115036 * A115038 A115039 A115040

Keyword

nonn,more

Author

Leroy Quet, Feb 26 2006

Extensions

More terms from Diana L. Mecum, Jun 02 2007

a(28)-a(40) from Michel Marcus, Sep 06 2019

a(41)-a(46) from Chai Wah Wu, May 19 2020

Status

approved