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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 21 2012
STATUS
approved