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A296431 Decimal expansion of ratio-sum for A296278; see Comments. 0
3, 4, 2, 7, 6, 7, 9, 9, 8, 5, 9, 6, 8, 2, 9, 5, 7, 8, 5, 3, 1, 4, 9, 6, 5, 6, 7, 0, 3, 6, 4, 5, 8, 0, 3, 9, 5, 7, 5, 2, 6, 9, 8, 8, 5, 8, 2, 6, 1, 7, 6, 8, 5, 6, 2, 4, 2, 6, 5, 4, 7, 2, 8, 3, 5, 1, 0, 5, 8, 5, 0, 8, 4, 6, 2, 6, 3, 4, 4, 6, 3, 6, 0, 6, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
2,1
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 ratio-sum for A is |a(1)/a(0) - g| + |a(2)/a(1) - g| + ..., assuming that this series converges. For A = A296278 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
EXAMPLE
ratio-sum = 34.27679985968295785314965...
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 - 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}]; (* A296278 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296278 *)
CROSSREFS
Sequence in context: A166108 A255768 A216221 * A045901 A098003 A026245
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 14 2017
STATUS
approved

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Last modified May 24 21:45 EDT 2024. Contains 372782 sequences. (Running on oeis4.)