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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). 6
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 (list; graph; refs; listen; history; text; internal format)
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 (zevi_35711(AT)yahoo.com), 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 * A230214 A284876 A216268

Adjacent sequences:  A132141 A132142 A132143 * A132145 A132146 A132147

KEYWORD

nonn

AUTHOR

Tanya Khovanova, Aug 12 2007

STATUS

approved

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Last modified August 24 02:32 EDT 2017. Contains 291052 sequences.