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A296428 Decimal expansion of ratio-sum for A295367; see Comments. 1
8, 8, 3, 9, 4, 4, 2, 6, 2, 1, 2, 7, 6, 4, 5, 1, 5, 3, 9, 7, 4, 9, 4, 4, 7, 3, 4, 0, 8, 4, 4, 1, 3, 0, 8, 1, 5, 6, 0, 3, 3, 1, 5, 6, 9, 0, 4, 1, 4, 6, 9, 1, 2, 9, 7, 0, 5, 3, 8, 5, 3, 9, 3, 9, 5, 9, 9, 9, 1, 4, 0, 5, 3, 9, 6, 9, 1, 3, 9, 1, 9, 5, 2, 1, 2, 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 = A295367, 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=1..86.

EXAMPLE

ratio-sum = 8.83944262127645153974944...

MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;

a[n_] := a[n] = a[n - 1] + a[n - 2] + b[n - 2]*b[n - 1];

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}]; (* A295367 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A296428 *)

CROSSREFS

Cf. A001622, A295367.

Sequence in context: A200686 A222066 A303617 * A073447 A011213 A178728

Adjacent sequences:  A296425 A296426 A296427 * A296429 A296430 A296431

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 14 2017

STATUS

approved

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Last modified March 28 03:39 EDT 2020. Contains 333073 sequences. (Running on oeis4.)