A296477 Decimal expansion of ratio-sum for A295950; see Comments.

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

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 = A295950, 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 = 4.289969273638318195483379960255534917753...

Mathematica

a[0] = 1; a[1] = 4; b[0] = 2; b[1 ] = 3; 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}]; (* A295950 *)
g = GoldenRatio; s = N[Sum[- g + a[n]/a[n - 1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100]  (* A296477 *)

Crossrefs

Cf. A001622, A296477, A296284, A296478.

Sequence in context: A195777 A125065 A109816 * A292964 A050128 A321119

Adjacent sequences: A296474 A296475 A296476 * A296478 A296479 A296480

Keyword

nonn,easy,cons

Author

Clark Kimberling, Jan 05 2018

Status

approved