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A205855
[s(k)-s(j)]/5, where the pairs (k,j) are given by A205852 and A205853, and s(k) denotes the (k+1)-st Fibonacci number.
3
1, 2, 1, 4, 10, 11, 22, 11, 46, 45, 44, 75, 121, 111, 197, 122, 319, 244, 122, 510, 499, 488, 836, 832, 1352, 1342, 1231, 2189, 2185, 1353, 3542, 3538, 2706, 1353, 5731, 5656, 5534, 5412, 9273, 9272, 9271, 9227, 15004, 14994, 14883, 13652
OFFSET
1,2
COMMENTS
For a guide to related sequences, see A205840.
EXAMPLE
The first six terms match these differences:
s(5)-s(3) = 8-3 = 5 = 5*1
s(6)-s(3) = 13-3 = 10 = 5*2
s(6)-s(5) = 13-8 = 5 = 5*1
s(7)-s(1) = 21-1 = 20 = 5*4
s(9)-s(4) = 55-5 = 50 = 5*10
s(10)-s(8) = 89-34 = 55 =5*11
MATHEMATICA
s[n_] := s[n] = Fibonacci[n + 1]; z1 = 500; 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 = 5; t = d[c] (* A205851 *)
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}] (* A205852 *)
Table[j[n], {n, 1, z2}] (* A205853 *)
Table[s[k[n]]-s[j[n]], {n, 1, z2}] (* A205854 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205855 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 02 2012
STATUS
approved