A204924 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k)=A000045(k+1) (Fibonacci numbers).

2, 3, 4, 4, 5, 5, 5, 6, 7, 6, 6, 6, 7, 9, 12, 7, 9, 7, 7, 7, 8, 10, 12, 12, 9, 8, 9, 10, 8, 17, 8, 8, 8, 9, 21, 12, 14, 10, 18, 17, 11, 9, 10, 10, 12, 12, 9, 12, 13, 9, 17, 9, 9, 9, 10, 17, 12, 12, 25, 22

Offset

1,1

Comments

See A204892 for a discussion and guide to related sequences.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

1 divides s(2)-s(1), so a(1)=2
2 divides s(3)-s(1), so a(2)=3
3 divides s(4)-s(2), so a(3)=4
9 divides s(7)-s(3), so a(9)=7

Mathematica

s[n_] := s[n] = Fibonacci[n + 1]; z1 = 300; z2 = 60;
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] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}]   (* A204923 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}]       (* A204924 *)
Table[j[n], {n, 1, z2}]       (* A204925 *)
Table[s[k[n]], {n, 1, z2}]    (* A204926 *)
Table[s[j[n]], {n, 1, z2}]    (* A204927 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204928 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204929 *)

Crossrefs

Cf. A000045, A204892.

Sequence in context: A130233 A131234 A349983 * A172006 A172005 A200247

Adjacent sequences: A204921 A204922 A204923 * A204925 A204926 A204927

Keyword

nonn

Author

Clark Kimberling, Jan 21 2012

Status

approved