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A298524
Decimal expansion of lim_ {n->oo} ((n+1)*g - s(0) - s(1) - ... - s(n)), where g = 1.790044015672757..., s(n) = (s(n - 1) + sqrt(2))^(1/2), s(0) = 1.
3
1, 1, 1, 9, 7, 9, 1, 8, 0, 7, 3, 0, 4, 6, 0, 8, 2, 9, 6, 5, 4, 6, 4, 8, 8, 9, 6, 0, 1, 0, 3, 9, 5, 5, 0, 5, 9, 1, 4, 1, 7, 9, 7, 9, 6, 3, 1, 6, 0, 8, 1, 0, 9, 1, 0, 2, 3, 9, 3, 8, 4, 0, 2, 5, 0, 8, 9, 8, 8, 2, 4, 5, 2, 1, 2, 6, 0, 9, 0, 8, 7, 9, 8, 6, 5, 8
OFFSET
1,4
COMMENTS
(lim_ {n->oo} s(n)) = g = positive zero of x^2 - x - sqrt(2). See A298512 for a guide to related sequences.
EXAMPLE
(n+1)*g - s(0) - s(1) - ... - s(n) -> 1.119791807304608296546488960103955059141...
MATHEMATICA
s[0] = 1; d = Sqrt[2]; 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]] (* A298524 *)
CROSSREFS
KEYWORD
nonn,easy,cons
AUTHOR
Clark Kimberling, Feb 12 2018
STATUS
approved