

A296452


Decimal expansion of limiting powerratio for A296245; see Comments.


25



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

2,1


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 = A296245 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=2..87.


EXAMPLE

Limiting powerratio = 35.92954925558318409021666878351219132071...


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;
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}] (* A296245 *)
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] (* A296452 *)


CROSSREFS

Cf. A001622, A296245.
Sequence in context: A186190 A019739 A101298 * A225594 A210946 A319984
Adjacent sequences: A296449 A296450 A296451 * A296453 A296454 A296455


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 15 2017


STATUS

approved



