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A296489 Decimal expansion of ratio-sum for A293358; see Comments. 3
3, 5, 3, 5, 9, 1, 7, 3, 9, 3, 5, 1, 5, 2, 5, 9, 3, 5, 0, 7, 1, 6, 8, 0, 2, 2, 3, 2, 2, 4, 8, 5, 5, 0, 6, 7, 3, 3, 5, 5, 7, 5, 3, 4, 6, 2, 2, 7, 4, 4, 6, 8, 4, 2, 8, 0, 2, 2, 1, 0, 8, 9, 2, 8, 7, 4, 5, 0, 0, 5, 1, 2, 4, 2, 3, 1, 0, 0, 6, 9, 4, 5, 5, 7, 8, 9 (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 = A293358, 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 = 3.535917393515259350716802232248550673355...

MATHEMATICA

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

a[n_] := a[n] = a[n - 1] + a[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}]; (* A293358 *)

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

Take[RealDigits[s, 10][[1]], 100]  (* A296489 *)

CROSSREFS

Cf. A001622, A293358, A296284, A296490.

Sequence in context: A228446 A188889 A219604 * A253398 A151568 A134429

Adjacent sequences:  A296486 A296487 A296488 * A296490 A296491 A296492

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Dec 19 2017

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)