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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000045, A001358, A049997, A132147.

Sequence in context: A300064 A039217 A239289 * A361634 A210490 A340682

Adjacent sequences: A131508 A131509 A131510 * A131512 A131513 A131514

Keyword

nonn

Author

Tanya Khovanova, Aug 14 2007

Status

approved