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A296477
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Decimal expansion of ratio-sum for A295950; see Comments.
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3
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4, 2, 8, 9, 9, 6, 9, 2, 7, 3, 6, 3, 8, 3, 1, 8, 1, 9, 5, 4, 8, 3, 3, 7, 9, 9, 6, 0, 2, 5, 5, 5, 3, 4, 9, 1, 7, 7, 5, 3, 3, 7, 3, 8, 4, 0, 6, 3, 1, 3, 9, 4, 4, 0, 3, 3, 8, 1, 3, 6, 5, 3, 4, 1, 0, 3, 3, 8, 5, 4, 0, 8, 0, 0, 4, 2, 2, 2, 2, 9, 7, 0, 9, 7, 2, 5
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OFFSET
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1,1
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COMMENTS
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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 = A295950, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.
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LINKS
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Table of n, a(n) for n=1..86.
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EXAMPLE
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ratio-sum = 4.289969273638318195483379960255534917753...
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MATHEMATICA
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a[0] = 1; a[1] = 4; b[0] = 2; b[1 ] = 3; b[2] = 5;
a[n_] := a[n] = a[n - 1] + a[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}]; (* A295950 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296477 *)
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CROSSREFS
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Cf. A001622, A296477, A296284, A296478.
Sequence in context: A195777 A125065 A109816 * A292964 A050128 A321119
Adjacent sequences: A296474 A296475 A296476 * A296478 A296479 A296480
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KEYWORD
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nonn,easy,cons
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AUTHOR
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Clark Kimberling, Jan 05 2018
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STATUS
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approved
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