A300004 First differences of the list A292794 of numbers not congruent to F(k) modulo F(k+1) for any k > 1, where F are the Fibonacci numbers A000045.

4, 2, 4, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 10, 2, 4, 2, 10, 2, 6, 4, 2, 4, 2, 4, 8, 6, 4, 2, 4, 2, 4, 6, 8, 4, 2, 6, 4, 6, 2, 6, 4, 2, 6, 4, 8, 6, 4, 6, 2, 4, 6, 2, 6, 6, 4, 2, 4, 6, 2, 6, 4, 2, 4, 2, 10, 8, 4, 2, 4, 2, 4, 8, 6, 4, 2, 4, 2, 10, 2, 6, 6, 10, 6, 2, 6, 4, 2, 4, 2, 4, 8, 6, 6, 4, 2, 4, 6, 2, 12, 4, 2, 4

Offset

0,1

Comments

The sequence has been chosen 0-indexed, as for A292794.

It has been conjectured that every even number occurs in this sequence.

It would be interesting to know whether there are patterns or formulae for the indices at which the respective even numbers occur.

The index of the first occurrence of 2n in this sequence is listed in A300004 = (1, 0, 5, 26, 14, ...): a(1), a(0), a(5), a(26), a(14), ... is the first occurrence of 2, 4, 6, 8, 10, ... in this sequence.

Links

Table of n, a(n) for n=0..103.

Formula

a(n) = A292794(n+1) - A292794(n).

Mathematica

Differences@ Join[{0}, Select[Range[3, 500], Function[n, NoneTrue[Block[{k = {1, 1}}, While[Last@k <= n, AppendTo[k, Total@ Take[k, -2]]]; Partition[Most@ k, 2, 1]], Mod[n, #2] == #1 & @@ # &]]]] (* Michael De Vlieger, Mar 19 2018 *)

Prog

(PARI) (D(v)=v[^1]-v[^-1])(A292794=select(is_A292794, [0..500]))
(PARI) print1(L=0); for(n=1, oo, is_A292794(n)&&print1(", ", -L+L=n))

Crossrefs

Cf. A292794, A000045.

Sequence in context: A373422 A328999 A236185 * A147973 A278527 A010474

Adjacent sequences: A300001 A300002 A300003 * A300005 A300006 A300007

Keyword

nonn

Author

M. F. Hasler, Feb 25 2018

Extensions

Edited by M. F. Hasler, Mar 05 2018

Status

approved