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A296474 Decimal expansion of limiting power-ratio for A295948; see Comments. 3
7, 4, 3, 2, 1, 3, 8, 6, 5, 6, 0, 2, 2, 4, 6, 4, 6, 9, 8, 6, 0, 3, 7, 4, 4, 7, 6, 2, 9, 9, 9, 1, 5, 0, 0, 0, 7, 5, 5, 1, 2, 5, 5, 0, 7, 1, 9, 6, 0, 8, 2, 8, 5, 9, 9, 8, 0, 3, 1, 0, 5, 5, 1, 5, 0, 6, 3, 4, 8, 4, 1, 8, 0, 3, 4, 0, 8, 6, 9, 6, 6, 3, 4, 8, 6, 3 (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 = A296948 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 = 7.432138656022464698603744762999150007551...

MATHEMATICA

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

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

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}]  (* A295948 *)

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] (* A296474 *)

CROSSREFS

Cf. A001622, A295948, A296473.

Sequence in context: A200121 A198348 A019857 * A194705 A344906 A243309

Adjacent sequences:  A296471 A296472 A296473 * A296475 A296476 A296477

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 19 2017

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)