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A296488 Decimal expansion of limiting power-ratio for A293076; see Comments. 3
4, 8, 6, 3, 6, 9, 8, 8, 6, 8, 1, 5, 6, 0, 7, 9, 1, 9, 5, 8, 5, 9, 8, 8, 8, 7, 5, 2, 1, 4, 9, 6, 5, 7, 1, 9, 8, 7, 1, 7, 4, 9, 0, 9, 2, 2, 2, 5, 6, 9, 4, 8, 8, 2, 3, 8, 9, 7, 6, 2, 2, 3, 2, 9, 1, 6, 7, 9, 6, 4, 4, 5, 0, 1, 6, 1, 7, 1, 3, 3, 9, 0, 8, 6, 3, 9 (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 = A293076, 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 = 4.863698868156079195859888752149657198717...

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 - 2];

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}]; (* A293076 *)

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]   (* A296488 *)

CROSSREFS

Cf. A001622, A293076, A296284, A296487.

Sequence in context: A193082 A201335 A219246 * A199294 A155741 A243376

Adjacent sequences:  A296485 A296486 A296487 * A296489 A296490 A296491

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 19 2017

STATUS

approved

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Last modified February 27 07:04 EST 2020. Contains 332299 sequences. (Running on oeis4.)