

A296430


Decimal expansion of ratiosum for A296272; see Comments.


1



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

2,2


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 ratiosum for A is a(1)/a(0)  g + a(2)/a(1)  g + . . . , assuming that this series converges. For A = A296272 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

ratiosum = 12.5831861005560957189096...


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  1]*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}]; (* A296272 *)
g = GoldenRatio; s = N[Sum[ g + a[n]/a[n  1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296430 *)


CROSSREFS

Cf. A001622, A296272.
Sequence in context: A131598 A220337 A198545 * A220398 A200225 A258749
Adjacent sequences: A296427 A296428 A296429 * A296431 A296432 A296433


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 14 2017


STATUS

approved



