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

1,2

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

Mathematica

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

Prog

(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

Crossrefs

Complement of A059389.

Sequence in context: A278034 A087657 A248478 * A179243 A350686 A064825

Adjacent sequences: A059387 A059388 A059389 * A059391 A059392 A059393

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved