A296482 Decimal expansion of limiting power-ratio for A295952; see Comments.

7, 0, 9, 0, 7, 0, 0, 6, 8, 7, 3, 5, 5, 1, 4, 2, 8, 8, 1, 1, 6, 7, 7, 4, 7, 5, 2, 6, 5, 0, 3, 3, 7, 1, 2, 1, 5, 9, 2, 1, 8, 4, 1, 1, 4, 6, 6, 7, 4, 7, 0, 1, 0, 3, 6, 6, 9, 0, 6, 0, 7, 5, 9, 3, 3, 6, 3, 2, 5, 5, 4, 8, 7, 9, 1, 6, 3, 6, 2, 1, 8, 8, 7, 8, 3, 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 limiting power-ratio for A is the limit as n->oo of a(n)/g^n, assuming that this limit exists. For A = A295952, 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 = 7.090700687355142881167747526503371215921...

Mathematica

a[0] = 1; a[1] = 5; b[0] = 2; b[1 ] = 3; b[2] = 4;
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}]; (* A295952 *)
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]   (* A296482 *)

Crossrefs

Cf. A001622, A295952, A296284, A296481.

Sequence in context: A178308 A320377 A213186 * A272429 A308157 A198555

Adjacent sequences: A296479 A296480 A296481 * A296483 A296484 A296485

Keyword

nonn,easy,cons

Author

Clark Kimberling, Jan 06 2018

Status

approved