

A131511


All possible products of prime and Fibonacci numbers.


1



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
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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(k8));
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 * A210490 A166155 A063538
Adjacent sequences: A131508 A131509 A131510 * A131512 A131513 A131514


KEYWORD

nonn


AUTHOR

Tanya Khovanova, Aug 14 2007


STATUS

approved



