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A296432 Decimal expansion of ratio-sum for A296284; see Comments. 1
6, 2, 1, 0, 3, 2, 7, 1, 0, 9, 4, 6, 6, 1, 8, 4, 9, 4, 2, 2, 7, 9, 6, 7, 9, 0, 4, 8, 4, 0, 2, 4, 2, 2, 4, 6, 0, 5, 4, 5, 3, 6, 8, 4, 1, 5, 7, 0, 9, 5, 7, 9, 1, 2, 3, 4, 0, 6, 9, 2, 7, 3, 5, 8, 7, 0, 5, 4, 0, 4, 4, 9, 1, 7, 0, 1, 8, 9, 8, 8, 8, 9, 6, 2, 7, 1 (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 ratio-sum for A is |a(1)/a(0) - g| + |a(2)/a(1) - g| + ..., assuming that this series converges. For A = A296284 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 = 6.21032710946618494227967...
MATHEMATICA
a[0] = 1; a[1] = 2; b[0] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + n*b[n - 2];
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}]; (* A296284 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296432 *)
CROSSREFS
Sequence in context: A182639 A244135 A120002 * A171542 A335587 A320302
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 15 2017
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)