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 A205845 [s(k)-s(j)]/3, where the pairs (k,j) are given by A205842 and A205843, and s(k) denotes the (k+1)-st Fibonacci number. 6
 1, 2, 1, 4, 6, 11, 7, 18, 14, 7, 29, 28, 27, 47, 41, 77, 76, 75, 48, 125, 124, 123, 96, 48, 203, 199, 192, 185, 328, 322, 281, 532, 528, 521, 514, 329, 861, 857, 850, 843, 658, 329, 1393, 1392, 1391, 1364, 1316, 1268, 2254, 2248, 2207, 1926, 3648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a guide to related sequences, see A205840. The first six terms match these differences: s(4)-s(2) = 5-2 = 3 = 3*1 s(5)-s(2) = 8-2 = 6 = 3*2 s(5)-s(4) = 8-5 = 3 = 3*1 s(6)-s(1) = 13-1 = 12 = 3*4 s(7)-s(3) = 21-3 = 18 = 3*6 s(8)-s(1) = 34-1 = 33 + 3*11 (See the program at A205842.) LINKS EXAMPLE The first six terms match these differences: s(4)-s(2) = 5-2 = 3 = 3*1 s(5)-s(2) = 8-2 = 6 = 3*2 s(5)-s(4) = 8-5 = 3 = 3*1 s(6)-s(1) = 13-1 = 12 = 3*4 s(7)-s(3) = 21-3 = 18 = 3*6 s(8)-s(1) = 34-1 = 33 + 3*11 MATHEMATICA s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; 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 = 3; t = d[c]       (* A205841 *) 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}]      (* A205842 *) Table[j[n], {n, 1, z2}]      (* A205843 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205844 *) Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205845 *) CROSSREFS Cf. A204890, A205842, A205845. Sequence in context: A283309 A054408 A285637 * A034424 A095012 A192781 Adjacent sequences:  A205842 A205843 A205844 * A205846 A205847 A205848 KEYWORD nonn AUTHOR Clark Kimberling, Feb 01 2012 STATUS approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)