A296480 Decimal expansion of limiting power-ratio for A295951; see Comments.

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

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 = 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

limiting power-ratio = 6.749918662049985424828699465394565293987...

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 *)
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]   (* A296480 *)

Crossrefs

Cf. A001622, A295951, A296284, A296479.

Sequence in context: A364356 A292101 A111969 * A021601 A305328 A332396

Adjacent sequences: A296477 A296478 A296479 * A296481 A296482 A296483

Keyword

nonn,easy,cons

Author

Clark Kimberling, Jan 05 2018

Status

approved