

A296492


Decimal expansion of limiting powerratio for A294170; see Comments.


4



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

2,3


COMMENTS

Suppose that A = (a(n)), for n >= 0, is a sequence, and g is a real number such that a(n)/a(n1) > g. The ratiosum for A is a(1)/a(0)  g + a(2)/a(1)  g + ..., assuming that this series converges. For A = A294170, 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=2..87.


EXAMPLE

limiting powerratio = 11.22071294787201913135639932120744822352...


MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; b[2] = 5;
a[n_] := a[n] = a[n  1] + a[n  2] + b[n] + 2 n;
j = 1; While[j < 16, k = a[j]  j  1;
While[k < a[j + 1]  j + 1, b[k] = j + k + 2; k++]; j++];
u = Table[a[n], {n, 0, k}]; (* A294170 *)
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] (* A296492 *)


CROSSREFS

Cf. A001622, A294381, A296284, A296491.
Sequence in context: A168615 A334921 A174104 * A135006 A323675 A243492
Adjacent sequences: A296489 A296490 A296491 * A296493 A296494 A296495


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 20 2017


STATUS

approved



