

A296427


Decimal expansion of ratiosum for A296257; see Comments.


1



7, 4, 8, 6, 5, 9, 8, 2, 3, 8, 8, 6, 1, 1, 7, 5, 1, 5, 0, 8, 3, 0, 4, 2, 2, 9, 1, 1, 8, 2, 1, 9, 2, 9, 6, 7, 7, 6, 4, 4, 6, 8, 2, 9, 9, 2, 3, 8, 9, 5, 1, 2, 3, 4, 6, 7, 0, 7, 0, 8, 2, 3, 7, 2, 0, 1, 3, 6, 8, 1, 1, 7, 6, 2, 5, 8, 9, 6, 9, 1, 6, 7, 0, 6, 1, 2
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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 ratiosum for A is a(1)/a(0)  g + a(2)/a(1)  g + . . . , assuming that this series converges. For A = A296257, 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 = 7.48659823886117515083042...


MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3;
a[n_] := a[n] = a[n  1] + a[n  2] + b[n  2]^2;
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}]; (* A296257 *)
g = GoldenRatio; s = N[Sum[ g + a[n]/a[n  1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296427 *)


CROSSREFS

Cf. A001622, A296257.
Sequence in context: A161166 A199060 A330596 * A092034 A153042 A330595
Adjacent sequences: A296424 A296425 A296426 * A296428 A296429 A296430


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Dec 14 2017


STATUS

approved



