A132146 -id:A132146 - cp's OEIS frontend

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

Tanya Khovanova, Aug 12 2007

nonn

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

			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.

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

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.

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 *)

A132147 Numbers that are the sum of a prime number and a positive Fibonacci number.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Offset: 1

Tanya Khovanova, Aug 12 2007

nonn

This sequence is a subsequence of A132145 and is the complement of A132146.
Lee shows that this sequence has positive lower density. - Charles R Greathouse IV, Nov 02 2010
The lower density of this sequence is at least 0.0254905 (Liu and Xue, 2021). - Amiram Eldar, Mar 04 2021

			11 = 3+8 is a term since it is the sum of a prime number (3) and a Fibonacci number (8).

T. D. Noe, Table of n, a(n) for n = 1..1000
K. S. Enoch Lee, On the sum of a prime and a Fibonacci number, International Journal of Number Theory, Vol. 6, No. 7 (2010), pp. 1669-1676; arXiv preprint, arXiv:1011.0173 [math.NT], 2010.
Zhixin Liu and Mengyuan Xue, The sum of a prime and a Fibonacci number, International Journal of Number Theory (2021).

Cf. A000040, A000045, A132145, A132146.

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

is(n)=my(k,f); while((f=fibonacci(k++))Charles R Greathouse IV, Sep 14 2015

cp's OEIS Frontend

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).

Views

Author

Keywords

Comments

Examples

References

Links

Programs

Mathematica