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

Author

Leroy Quet, Feb 26 2006

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000045, A001605, A060385.

Programs

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

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