_Clark Kimberling (ck6(AT)evansville.edu), _, Jan 27 2012

proposed

approved

editing

proposed

allocated Least k such that n divides s(k)-s(j) for Clark Kimberlingsome j<k, where s(j) is the 2j-th Fibonacci number.

2, 2, 4, 4, 3, 4, 3, 6, 4, 4, 6, 8, 4, 7, 12, 9, 5, 4, 10, 4, 8, 7, 7, 8, 13, 5, 5, 9, 8, 14, 16, 15, 12, 5, 11, 12, 10, 10, 16, 9, 6, 8, 12, 16, 14, 7, 5, 12, 10, 14, 20, 5, 14, 5, 10, 9, 20, 8, 30, 32

1,1

See A204892 for a discussion and guide to related sequences.

Least k such that n divides s(k)-s(j) for some j<k, where s(j) is the 2j-th Fibonacci number.

See A204892 for a discussion and guide to related sequences.

s[n_] := s[n] = Fibonacci[2*n]; z1 = 500; z2 = 60;

Table[s[n], {n, 1, 30}] (* A001906 *)

u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]

Table[u[m], {m, 1, z1}] (* A205448 *)

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}] (* A205449 *)

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}] (* A205450 *)

Table[j[n], {n, 1, z2}] (* A205451 *)

Table[s[k[n]], {n, 1, z2}] (* A205452 *)

Table[s[j[n]], {n, 1, z2}] (* A205453 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205454 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205455 *)

Cf. A001906, A205455, A204892.

allocated

nonn

Clark Kimberling (ck6(AT)evansville.edu), Jan 27 2012

approved

editing

allocated for Clark Kimberling

allocated

approved