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A296486 Decimal expansion of limiting power-ratio for A295960; see Comments. 3
5, 8, 5, 9, 9, 9, 6, 6, 2, 9, 8, 4, 4, 6, 4, 4, 0, 3, 1, 2, 8, 6, 0, 3, 5, 7, 7, 5, 8, 6, 0, 5, 4, 2, 6, 0, 8, 8, 1, 6, 1, 8, 8, 8, 4, 6, 3, 9, 7, 2, 6, 3, 6, 1, 0, 1, 9, 6, 8, 1, 0, 0, 1, 8, 7, 9, 9, 3, 6, 3, 9, 4, 8, 0, 6, 9, 6, 5, 7, 1, 0, 4, 5, 7, 9, 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 = A295960, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

limiting power-ratio = 5.859996629844644031286035775860542608816...

MATHEMATICA

a[0] = 1; a[1] = 3; b[0] = 2; b[1 ] = 4; b[2] = 5;

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

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}]; (* A295960 *)

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]   (* A296486 *)

CROSSREFS

Cf. A001622, A295960, A296284, A296485.

Sequence in context: A273817 A073212 A059742 * A011424 A011495 A136258

Adjacent sequences:  A296483 A296484 A296485 * A296487 A296488 A296489

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Apr 13 2018

STATUS

approved

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Last modified November 13 17:34 EST 2019. Contains 329106 sequences. (Running on oeis4.)