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A205837 Numbers k for which 2 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number. 4
3, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For a guide to related sequences, see A205840.
LINKS
EXAMPLE
The first six terms match these differences:
s(3)-s(1) = 3-1 = 2
s(4)-s(1) = 5-1 = 4
s(4)-s(3) = 5-3 = 2
s(5)-s(2) = 8-2 = 6
s(6)-s(1) = 13-1 = 12
s(6)-s(3) = 13-3 = 10
MATHEMATICA
s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A204922 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 2; t = d[c] (* A205556 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205837 *)
Table[j[n], {n, 1, z2}] (* A205838 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}](* A205839 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}](* A205840 *)
CROSSREFS
Sequence in context: A198300 A054760 A079107 * A262872 A257923 A288178
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 01 2012
STATUS
approved

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Last modified June 22 04:48 EDT 2024. Contains 373565 sequences. (Running on oeis4.)