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A296847 Decimal expansion of ratio-sum for A296846; see Comments. 2
2, 5, 1, 3, 4, 8, 8, 7, 0, 3, 3, 6, 6, 4, 2, 1, 5, 6, 2, 0, 4, 4, 5, 4, 9, 0, 9, 4, 9, 3, 9, 1, 3, 9, 1, 5, 2, 1, 9, 1, 7, 5, 6, 9, 4, 4, 3, 0, 5, 3, 6, 7, 3, 0, 6, 5, 3, 1, 7, 8, 9, 8, 7, 7, 2, 3, 6, 5, 3, 9, 9, 9, 5, 2, 4, 6, 1, 8, 4, 0, 4, 0, 7, 2, 9, 2 (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 = A296846, 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 = 2.513488703366421562044549094939139152191...

MATHEMATICA

a[0] = 3; a[1] = 5; b[0] = 1; b[1] = 2; b[2] = 4;

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

j = 1; While[j < 16, k = a[j] - j - 1;

While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++];

u = Table[a[n], {n, 0, k}];  (* A296846 *)

g = GoldenRatio; s = N[Sum[g - a[n]/a[n - 1], {n, 1, 1000}], 200];  (* A296847 *)

StringJoin[StringTake[ToString[s], 41], "..."]

Take[RealDigits[s, 10][[1]], 100] (* A296847 *)

CROSSREFS

Cf. A001622, A296846, A296848.

Sequence in context: A011456 A233384 A186692 * A100084 A269598 A100226

Adjacent sequences:  A296844 A296845 A296846 * A296848 A296849 A296850

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Jan 12 2018

STATUS

approved

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Last modified June 19 00:55 EDT 2019. Contains 324217 sequences. (Running on oeis4.)