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 A297012 Decimal expansion of ratio-sum for A297011; see Comments. 2
 2, 5, 1, 8, 4, 3, 9, 3, 4, 6, 0, 1, 2, 6, 2, 3, 9, 0, 0, 8, 9, 6, 8, 3, 7, 6, 4, 1, 1, 9, 1, 5, 5, 0, 6, 9, 1, 0, 1, 6, 3, 9, 3, 9, 8, 8, 1, 8, 7, 7, 7, 0, 4, 7, 5, 8, 6, 1, 5, 9, 6, 2, 5, 0, 9, 1, 5, 1, 5, 0, 9, 0, 9, 6, 8, 6, 3, 8, 2, 8, 2, 8, 1, 9, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 = A297011, we have g = 1 + sqrt(2). See A296425-A296434 for related ratio-sums and A296452-A296461 for related limiting power-ratios. LINKS EXAMPLE ratio-sum = 2.518439346012623900896837641191550691016... MATHEMATICA a[0] = 3; a[1] = 5; b[0] = 1; b[1] = 2; b[2] = 4; a[n_] := a[n] = 2 a[n - 1] + a[n - 2] - b[n]; j = 1; While[j < 9, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; u = Table[a[n], {n, 0, k}]; (* A297011 *) r = 1 + Sqrt[2]; s = N[Sum[r - a[n]/a[n - 1], {n, 1, 1000}], 200]; StringJoin[StringTake[ToString[s], 41], "..."] Take[RealDigits[s, 10][[1]], 100] (* A297012 *) CROSSREFS Cf. A297011. Sequence in context: A124576 A283556 A268980 * A259449 A174815 A021401 Adjacent sequences:  A297009 A297010 A297011 * A297013 A297014 A297015 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Jan 13 2018 STATUS approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)