A290748 Let F denote the two-way infinite sequence of Fibonacci numbers (for all positive or negative integers k, F(k+2)=F(k)+F(k+1) with F(0)=0, F(1)=1). Sequence lists positive numbers that are the difference between two terms of F.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 26, 29, 31, 32, 33, 34, 35, 37, 42, 47, 50, 52, 53, 54, 55, 56, 57, 58, 60, 63, 68, 76, 81, 84, 86, 87, 88, 89, 90, 92, 97, 110, 123, 131, 136, 139, 141, 142, 143, 144, 145, 146

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Don Reble, Difference of Fibonacci's, Posting to Sequence Fans Mailing List, Aug 10 2017.

Example

9 is here because F(6) - F(-2) = 8 - (-1) = 9.

Maple

N:= 40: # to get all terms <= F(N) - F(N-1)
P:= sort(convert({seq(combinat:-fibonacci(n), n=-N..N)}, list)):
sort(convert(select(`<=`, {seq(seq(P[i]-P[j], j=1..i-1), i=1..nops(P))}, P[-1]-P[-2]), list)): # Robert Israel, Aug 11 2017

Mathematica

Select[Union[Subtract @@@ Tuples[Fibonacci[Range[-30, 30]], 2]], 0 < # < 150 &] (* Giovanni Resta, Aug 11 2017 *)

Crossrefs

Cf. A000045, A007298 (if we only use F(k) for k >= 0).

See A290749 for the complement.

Sequence in context: A348519 A061773 A125007 * A035062 A032964 A033066

Adjacent sequences: A290745 A290746 A290747 * A290749 A290750 A290751

Keyword

nonn

Author

N. J. A. Sloane, Aug 11 2017

Extensions

Corrected by R. J. Mathar, Aug 10 2017

More terms from Giovanni Resta, Aug 11 2017

Status

approved