

A290748


Let F denote the twoway 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.


2



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
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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(N1)
P:= sort(convert({seq(combinat:fibonacci(n), n=N..N)}, list)):
sort(convert(select(`<=`, {seq(seq(P[i]P[j], j=1..i1), 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: A179892 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



