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A296497 Decimal expansion of ratio-sum for A294541; see Comments. 3
3, 4, 8, 9, 8, 0, 1, 8, 3, 9, 1, 6, 5, 1, 8, 0, 8, 8, 3, 9, 3, 9, 5, 8, 4, 0, 8, 2, 8, 8, 2, 5, 7, 1, 7, 2, 3, 7, 6, 9, 1, 6, 5, 8, 1, 9, 0, 7, 5, 4, 7, 8, 7, 6, 4, 0, 7, 4, 9, 9, 5, 3, 8, 4, 0, 5, 7, 0, 2, 8, 6, 8, 7, 8, 0, 0, 5, 7, 0, 3, 3, 7, 8, 9, 5, 3 (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 = A294541, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.
LINKS
EXAMPLE
3.489801839165180883939584082882571723769...
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 - 1] + b[n - 2];
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}]; (* A294541 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296497 *)
CROSSREFS
Sequence in context: A075562 A316137 A089290 * A019811 A075746 A342791
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Dec 20 2017
STATUS
approved

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Last modified February 23 13:42 EST 2024. Contains 370283 sequences. (Running on oeis4.)