A059390 Numbers that are not the sum of two nonzero Fibonacci numbers.

1, 12, 17, 19, 20, 25, 27, 28, 30, 31, 32, 33, 38, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 93, 95, 96, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109

Offset: 1

Author

Avi Peretz (njk(AT)netvision.net.il), Jan 29 2001

Keywords

• nonn
• easy

Comments

Except for the initial 1, each term can be expressed as the sum of a Fibonacci number and a non-Fibonacci number (A001690) and is thus the sum of three or more Fibonacci numbers. - Alonso del Arte, Jun 18 2013

That is, aside from the first term, numbers n such that A007895(n) > 2. - Charles R Greathouse IV, Jun 18 2013

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A059389.

Programs

Mathematica

Complement[ Range[ Fibonacci[ 12 ]], Union[ Flatten[ Table[ Fibonacci[i] + Fibonacci[j], {i, 12}, {j, i - 1}]]]] (* Robert G. Wilson v, Jul 22 2005 *)

PARI

is(n)=if(n<9,return(n==1)); my(k);while(fibonacci(k++)<=n,); n-=fibonacci(k-1); k=n^2; k+=(k+1)<<2; !issquare(k) && !issquare(k-8) \\ Charles R Greathouse IV, Jun 18 2013

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jan 31 2001