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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). 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A204892 for a discussion and guide to related sequences.

LINKS

Table of n, a(n) for n=1..60.

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: A049839 A130233 A131234 * A172006 A172005 A200247

Adjacent sequences:  A204921 A204922 A204923 * A204925 A204926 A204927

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 21 2012

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)