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A296453 Decimal expansion of limiting power-ratio for A296251; see Comments. 1
2, 7, 0, 9, 7, 1, 7, 3, 6, 3, 7, 1, 6, 1, 3, 7, 3, 1, 8, 8, 6, 1, 4, 3, 6, 9, 2, 3, 1, 6, 0, 0, 8, 5, 3, 0, 9, 3, 6, 3, 8, 6, 6, 0, 5, 9, 5, 9, 1, 4, 1, 6, 1, 9, 8, 9, 1, 8, 8, 7, 3, 5, 6, 8, 0, 2, 8, 5, 4, 7, 4, 3, 7, 7, 7, 1, 9, 4, 2, 7, 0, 9, 9, 0, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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 = A296251 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

Table of n, a(n) for n=2..87.

EXAMPLE

Limiting power-ratio = 27.09717363716137318861436923160085309363...

MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;

a[n_] := a[n] = a[n - 1] + a[n - 2] + b[n - 1]^2;

j = 1; While[j < 12, k = a[j] - j - 1;

While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++];

Table[a[n], {n, 0, 15}]  (* A296251 *)

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] (* A296453 *)

CROSSREFS

Cf. A001622, A296251.

Sequence in context: A245224 A016638 A199398 * A011294 A282072 A282493

Adjacent sequences:  A296450 A296451 A296452 * A296454 A296455 A296456

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 15 2017

STATUS

approved

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Last modified May 20 20:16 EDT 2019. Contains 323426 sequences. (Running on oeis4.)