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A298532
Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.866760399173862092990..., s(n) = (s(n - 1) + tau)^(1/2), s(0) = tau = (1+sqrt(5))/2 (golden ratio).
2
3, 4, 1, 5, 3, 3, 3, 9, 8, 0, 5, 2, 9, 0, 5, 7, 3, 2, 1, 9, 5, 0, 4, 3, 4, 3, 7, 0, 6, 6, 2, 3, 3, 3, 0, 6, 0, 7, 7, 0, 1, 2, 2, 2, 7, 4, 7, 1, 1, 6, 1, 5, 0, 3, 8, 9, 0, 1, 9, 9, 5, 2, 7, 0, 5, 0, 4, 8, 6, 6, 6, 5, 4, 5, 1, 9, 1, 9, 1, 7, 3, 0, 0, 2, 4, 5
OFFSET
0,1
COMMENTS
(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - tau. See A298512 for a guide to related sequences.
EXAMPLE
lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)) -> 0.3415333980529057321950...
MATHEMATICA
tau = GoldenRatio;
s[0] = tau; d = tau; p = 1/2;
g = (x /. NSolve[x^(1/p) - x - d == 0, x, 200])[[2]]
s[n_] := s[n] = (s[n - 1] + d)^p
N[Table[s[n], {n, 0, 30}]]
s = N[Sum[g - s[n], {n, 0, 200}], 150 ];
RealDigits[s, 10][[1]] (* A298532 *)
CROSSREFS
Sequence in context: A079529 A361508 A299022 * A133779 A137911 A019599
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Feb 13 2018
STATUS
approved