A296479 Decimal expansion of ratio-sum for A295951; see Comments.

2, 5, 7, 1, 9, 7, 1, 3, 6, 9, 3, 0, 7, 5, 7, 8, 2, 4, 5, 3, 4, 0, 6, 7, 2, 4, 8, 9, 6, 7, 2, 0, 8, 7, 6, 5, 9, 8, 7, 6, 8, 8, 8, 2, 5, 4, 5, 3, 3, 3, 9, 6, 3, 8, 1, 9, 6, 8, 6, 9, 0, 7, 4, 2, 8, 4, 3, 0, 5, 5, 0, 2, 3, 7, 4, 6, 4, 3, 3, 1, 8, 4, 7, 3, 5, 0

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 = A295951, 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 = 2.571971369307578245340672489672087659876...

Mathematica

a[0] = 2; a[1] = 3; b[0] = 1; b[1 ] = 4; 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}]; (* A295951 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100]  (* A296479 *)

Crossrefs

Cf. A001622, A295951, A296284, A296480.

Sequence in context: A181583 A010589 A024715 * A354088 A024709 A101245

Adjacent sequences: A296476 A296477 A296478 * A296480 A296481 A296482

Keyword

nonn,easy,cons

Author

Clark Kimberling, Jan 05 2018

Status

approved