A132144 Numbers that can't be expressed as the sum of a prime number and a Fibonacci number (0 is considered to be a Fibonacci number).

1, 35, 119, 125, 177, 208, 209, 221, 255, 287, 299, 329, 363, 416, 485, 515, 519, 535, 539, 551, 561, 567, 637, 697, 705, 718, 755, 768, 779, 784, 793, 815, 869, 875, 899, 925, 926, 933, 935, 951, 995, 1037, 1045, 1075, 1079, 1107, 1139, 1145, 1147, 1149

Offset

1,2

Comments

This sequence is a subsequence of A132146 and the complement of A132145.

References

J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 76-79. ASIN: B002ACVZ6O [From Jason Earls, Nov 24 2009]

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Lenny Jones, Fibonacci variations of a conjecture of Polignac, Integers, 12 (2012), A11.

Example

The smallest prime number is 2, the smallest Fibonacci number is 0; hence 1 can't be presented as a sum of a prime number and a Fibonacci number.

Mathematica

nn = 17; f = Union[Fibonacci[Range[0, nn]]]; p = Prime[Range[PrimePi[f[[-1]]]]]; fp = Select[Union[Flatten[Outer[Plus, f, p]]], # < f[[-1]] &]; Complement[Range[f[[-1]] - 1], fp] (* T. D. Noe, Mar 06 2012 *)

Crossrefs

Sequence in context: A044286 A044667 A262455 * A337233 A230214 A284876

Adjacent sequences: A132141 A132142 A132143 * A132145 A132146 A132147

Keyword

nonn

Author

Tanya Khovanova, Aug 12 2007

Status

approved