

A296458


Decimal expansion of limiting powerratio for A296278; see Comments.


1



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

3,2


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 limiting powerratio for A is the limit as n>oo of a(n)/g^n, assuming that this limit exists. For A = A296278 we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See A296425A296434 for related ratiosums and A296452A296461 for related limiting powerratios.


LINKS

Table of n, a(n) for n=3..88.


EXAMPLE

Limiting powerratio = 190.0607530933015238869680838294138589000...


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]*b[n  1]*b[n  2];
j = 1; While[j < 12, k = a[j]  j  1;
While[k < a[j + 1]  j + 1, b[k] = j + k + 2; k++]; j++];
Table[a[n], {n, 0, 15}] (* A296278 *)
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] (* A296458 *)


CROSSREFS

Cf. A001622, A296278.
Sequence in context: A254968 A019940 A257435 * A199870 A132267 A021115
Adjacent sequences: A296455 A296456 A296457 * A296459 A296460 A296461


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 15 2017


STATUS

approved



