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 A296494 Decimal expansion of limiting power-ratio for A296555; see Comments. 3
 8, 6, 4, 3, 4, 8, 6, 8, 8, 6, 5, 5, 1, 7, 4, 8, 8, 3, 1, 6, 8, 2, 9, 8, 8, 6, 6, 6, 2, 5, 1, 4, 3, 6, 4, 4, 6, 9, 7, 9, 9, 2, 5, 0, 7, 9, 3, 2, 1, 0, 3, 4, 1, 3, 3, 5, 6, 0, 9, 9, 5, 5, 9, 6, 5, 1, 8, 1, 8, 3, 9, 1, 8, 0, 0, 4, 6, 8, 8, 6, 1, 7, 9, 8, 7, 5 (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 limiting power-ratio for A is the limit as n->oo of a(n)/g^n, assuming that this limit exists. For A = A296555, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences. LINKS EXAMPLE limiting power-ratio = 8.643486886551748831682988666251436446979... 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] + n; 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}]; (* A296555 *) z = 2000; g = GoldenRatio; h = Table[N[a[n]/g^n, z], {n, 0, z}]; StringJoin[StringTake[ToString[h[[z]]], 41], "..."] Take[RealDigits[Last[h], 10][[1]], 120]   (* A296494 *) CROSSREFS Cf. A001622, A296284, A296493, A296555. Sequence in context: A333198 A093019 A175573 * A261027 A296041 A008569 Adjacent sequences:  A296491 A296492 A296493 * A296495 A296496 A296497 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Dec 19 2017 STATUS approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)