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A296430 Decimal expansion of ratio-sum for A296272; see Comments. 1
1, 2, 5, 8, 3, 1, 8, 6, 1, 0, 0, 5, 5, 6, 0, 9, 5, 7, 1, 8, 9, 0, 9, 6, 6, 0, 8, 2, 7, 9, 6, 6, 1, 1, 9, 8, 7, 5, 4, 5, 9, 4, 1, 1, 2, 9, 8, 2, 6, 3, 1, 7, 9, 2, 5, 1, 5, 2, 0, 0, 3, 8, 0, 0, 0, 8, 1, 2, 9, 4, 3, 5, 1, 5, 9, 8, 0, 7, 3, 0, 7, 0, 3, 1, 1, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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 = A296272 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

ratio-sum = 12.5831861005560957189096...

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 - 1]*b[n];

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}]; (* A296272 *)

g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]

Take[RealDigits[s, 10][[1]], 100]  (* A296430 *)

CROSSREFS

Cf. A001622, A296272.

Sequence in context: A131598 A220337 A198545 * A220398 A200225 A258749

Adjacent sequences:  A296427 A296428 A296429 * A296431 A296432 A296433

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 14 2017

STATUS

approved

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)