

A296497


Decimal expansion of ratiosum for A294541; see Comments.


3



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

1,1


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 = A294541, we have g = (1 + sqrt(5))/2, the golden ratio (A001622). See the guide at A296469 for related sequences.


LINKS



EXAMPLE

3.489801839165180883939584082882571723769...


MATHEMATICA

a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
a[n_] := a[n] = a[n  1] + a[n  2] + b[n  1] + b[n  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}]; (* A294541 *)
g = GoldenRatio; s = N[Sum[ g + a[n]/a[n  1], {n, 1, 1000}], 200]
Take[RealDigits[s, 10][[1]], 100] (* A296497 *)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



