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 A205872 Numbers k for which 9 divides s(k)-s(j) for some j
 7, 9, 10, 12, 12, 13, 13, 13, 14, 16, 17, 17, 18, 19, 20, 21, 21, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 29, 29, 29, 30, 30, 31, 31, 31, 32, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For a guide to related sequences, see A205840. LINKS EXAMPLE The first six terms match these differences: s(7)-s(3) = 21-3 = 18 = 9*2 s(9)-s(1) = 55-1 = 54 = 9*6 s(10)-s(5) = 89-8 = 81 = 9*9 s(12)-s(5) = 233-8 = 225 = 9*25 s(12)-s(10) = 233-89 = 144 = 9*16 s(13)-s(5) = 377-8 = 369 =9*41 MATHEMATICA s[n_] := s[n] = Fibonacci[n + 1]; z1 = 600; z2 = 50; 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 = 9; t = d[c]     (* A205871 *) 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}]       (* A205872 *) Table[j[n], {n, 1, z2}]         (* A205873 *) Table[s[k[n]] - s[j[n]], {n, 1, z2}]   (* A205874 *) Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205875 *) CROSSREFS Cf. A204892, A205873, A205875. Sequence in context: A043397 A008536 A031000 * A248636 A151913 A095034 Adjacent sequences:  A205869 A205870 A205871 * A205873 A205874 A205875 KEYWORD nonn AUTHOR Clark Kimberling, Feb 02 2012 STATUS approved

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Last modified August 9 15:33 EDT 2022. Contains 356026 sequences. (Running on oeis4.)