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
Keywords
Examples
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.
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.
Programs
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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 *)
Comments