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 A296476 Decimal expansion of limiting power-ratio for A295949; see Comments. 3
 6, 1, 3, 6, 3, 8, 5, 5, 1, 8, 6, 6, 6, 2, 2, 0, 7, 9, 0, 9, 5, 5, 3, 4, 3, 9, 4, 9, 1, 5, 2, 6, 3, 6, 1, 2, 4, 4, 6, 0, 1, 1, 9, 2, 3, 6, 9, 8, 1, 2, 8, 5, 1, 9, 0, 7, 9, 6, 7, 5, 7, 1, 7, 2, 0, 2, 5, 9, 9, 5, 3, 7, 2, 2, 4, 5, 5, 6, 5, 5, 6, 2, 6, 0, 6, 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 limiting power-ratio for A is the limit as n->oo of a(n)/g^n, assuming that this limit exists. For A = A295949, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences. LINKS EXAMPLE limiting power-ratio = 6.136385518666220790955343949152636124460... 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]; 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}]; (* A295949 *) 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]   (* A296476 *) CROSSREFS Cf. A001622, A295949, A296284, A296475. Sequence in context: A085677 A321093 A219552 * A296504 A188859 A074584 Adjacent sequences:  A296473 A296474 A296475 * A296477 A296478 A296479 KEYWORD nonn,easy,cons AUTHOR Clark Kimberling, Dec 19 2017 EXTENSIONS Definition and sequence corrected by Clark Kimberling, Jan 05 2018 STATUS approved

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Last modified April 1 02:00 EDT 2020. Contains 333153 sequences. (Running on oeis4.)