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A296473 Decimal expansion of ratio-sum for A295948; see Comments. 3
1, 9, 1, 6, 9, 7, 8, 1, 0, 6, 7, 4, 3, 3, 0, 0, 9, 2, 8, 4, 3, 4, 3, 2, 3, 0, 5, 8, 9, 7, 4, 4, 1, 8, 6, 0, 8, 1, 2, 1, 0, 1, 4, 8, 6, 7, 3, 4, 8, 9, 3, 4, 8, 1, 6, 8, 6, 2, 1, 7, 8, 6, 1, 9, 0, 5, 3, 1, 1, 3, 9, 4, 9, 7, 7, 9, 9, 8, 6, 6, 6, 0, 6, 0, 4, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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 = A295948, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.

LINKS

Table of n, a(n) for n=1..86.

EXAMPLE

ratio-sum = 1.916978106743300928434323058974418608121...

MATHEMATICA

a[0] = 3; a[1] = 4; b[0] = 1; b[1 ] = 2; 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}]; (* A295948 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A296473 *)

CROSSREFS

Cf. A001622, A295948, A296284, A296474.

Sequence in context: A160042 A264934 A195712 * A213916 A297815 A021920

Adjacent sequences:  A296470 A296471 A296472 * A296474 A296475 A296476

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 19 2017

STATUS

approved

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Last modified January 20 23:24 EST 2020. Contains 331104 sequences. (Running on oeis4.)