A131511 All possible products of prime and Fibonacci numbers.

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 25, 26, 29, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 73, 74, 79, 82, 83, 85, 86, 87, 88, 89, 91, 93, 94, 95, 97, 101, 102, 103, 104, 105

Offset: 1

Author

Tanya Khovanova, Aug 14 2007

Keywords

• nonn

Comments

This sequence contains all prime numbers as a subsequence because 1 is a Fibonacci number. Similarly it contains all even semiprimes.

Examples

			8 is not in this sequence because the only way to represent 8 as a product of a prime and some number is 2*4 and 4 is not a Fibonacci number.
105 is in this sequence because 105 = 3*21 and 3 is a prime number and 21 is a Fibonacci number.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000045, A001358, A049997, A132147.

Programs

Mathematica

Take[Union[Flatten[Table[Fibonacci[n]*Prime[k], {n, 70}, {k, 70}]]], 70]

PARI

isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(n) = {if (n==0, return (1)); my(f=factor(n)); for (k=1, #f~, p = f[k, 1]; if (isfib(n/p), return (1)););} \\ Michel Marcus, Apr 19 2018