A296478 Decimal expansion of limiting power-ratio for A295950; see Comments.

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

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 limiting power-ratio for A is the limit as n->oo of a(n)/g^n, assuming that this limit exists. 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

limiting power-ratio = 6.920208311693159108588213408494198705738...

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 *)
z = 2000; g = GoldenRatio; h = Table[N[a[n]/g^n, z], {n, 0, z}];
StringJoin[StringTake[ToString[h[[z]]], 41], "..."]
Take[RealDigits[Last[h], 10][[1]], 120]   (* A296478 *)

Crossrefs

Cf. A001622, A295950, A296284, A296477.

Sequence in context: A011454 A274480 A115145 * A195403 A021595 A197696

Adjacent sequences: A296475 A296476 A296477 * A296479 A296480 A296481

Keyword

nonn,easy,cons

Author

Clark Kimberling, Jan 05 2018

Status

approved