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A296492 Decimal expansion of limiting power-ratio for A294170; see Comments. 4
1, 1, 2, 2, 0, 7, 1, 2, 9, 4, 7, 8, 7, 2, 0, 1, 9, 1, 3, 1, 3, 5, 6, 3, 9, 9, 3, 2, 1, 2, 0, 7, 4, 4, 8, 2, 2, 3, 5, 2, 3, 0, 1, 4, 9, 2, 6, 1, 9, 0, 4, 2, 5, 0, 7, 7, 3, 3, 5, 9, 0, 7, 6, 1, 3, 8, 9, 6, 1, 1, 3, 4, 2, 2, 3, 5, 4, 8, 8, 0, 1, 0, 7, 9, 7, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,3

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 ratio-sum for A is |a(1)/a(0) - g| + |a(2)/a(1) - g| + ..., assuming that this series converges. For A = A294170, 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=2..87.

EXAMPLE

limiting power-ratio = 11.22071294787201913135639932120744822352...

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] + 2 n;

j = 1; While[j < 16, k = a[j] - j - 1;

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

u = Table[a[n], {n, 0, k}];  (* A294170 *)

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]   (* A296492 *)

CROSSREFS

Cf. A001622, A294381, A296284, A296491.

Sequence in context: A168615 A334921 A174104 * A135006 A323675 A243492

Adjacent sequences:  A296489 A296490 A296491 * A296493 A296494 A296495

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 20 2017

STATUS

approved

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Last modified June 2 07:15 EDT 2020. Contains 334767 sequences. (Running on oeis4.)