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A296429 Decimal expansion of ratio-sum for A296266; see Comments. 1
1, 0, 2, 4, 2, 8, 9, 3, 9, 1, 0, 1, 2, 1, 3, 0, 3, 6, 7, 9, 8, 3, 4, 8, 7, 2, 4, 7, 4, 6, 0, 2, 4, 3, 8, 2, 2, 5, 2, 4, 6, 5, 0, 8, 6, 4, 0, 9, 5, 2, 2, 0, 7, 1, 6, 7, 7, 6, 2, 4, 8, 6, 4, 6, 5, 3, 9, 9, 7, 1, 7, 3, 6, 9, 3, 7, 7, 7, 9, 9, 7, 0, 4, 5, 3, 1 (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 = A296266, 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 = 10.24289391012130367983487...

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]*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}]; (* A296266 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A296429 *)

CROSSREFS

Cf. A001622, A296266.

Sequence in context: A152874 A324716 A328378 * A065286 A068217 A303603

Adjacent sequences:  A296426 A296427 A296428 * A296430 A296431 A296432

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 14 2017

STATUS

approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)