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 A296425 Decimal expansion of ratio-sum for A296245; see Comments. 25
 1, 4, 9, 7, 6, 3, 2, 7, 1, 4, 4, 8, 5, 6, 3, 0, 4, 1, 2, 4, 1, 1, 6, 8, 9, 6, 3, 5, 6, 2, 6, 9, 8, 7, 9, 3, 6, 1, 3, 5, 1, 0, 5, 0, 4, 8, 2, 1, 7, 4, 9, 2, 0, 3, 2, 2, 3, 6, 7, 0, 3, 3, 5, 7, 8, 3, 0, 6, 8, 4, 9, 2, 4, 3, 3, 2, 4, 0, 5, 8, 2, 6, 9, 4, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n-1) -> g. The ratio-sum for A is |a(1)/a(0) - g| + |a(2)/a(1) - g| + ..., assuming that this series converges. For A = A296245, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See A296425-A296434 for related ratio-sums and A296452-A296461 for related limiting power-ratios. LINKS EXAMPLE 14.9763271448563041241168963... MATHEMATICA a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5; a[n_] := a[n] = a[n - 1] + a[n - 2] + b[n]^2; j = 1; While[j < 13, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; Table[a[n], {n, 0, k}]; (* A296245 *) g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200] Take[RealDigits[s, 10][[1]], 100]  (* A296425 *) CROSSREFS Cf. A001622, A296245. Sequence in context: A245670 A166923 A021205 * A335089 A306004 A056992 Adjacent sequences:  A296422 A296423 A296424 * A296426 A296427 A296428 KEYWORD nonn,easy,cons,changed AUTHOR Clark Kimberling, Dec 14 2017 STATUS approved

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Last modified July 26 20:56 EDT 2021. Contains 346300 sequences. (Running on oeis4.)