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
Keywords
Examples
9 is here because F(6) - F(-2) = 8 - (-1) = 9.
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.
Programs
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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 *)
Extensions
Corrected by R. J. Mathar, Aug 10 2017
More terms from Giovanni Resta, Aug 11 2017