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A354771
Sum-critical values for the divergent series Sum_{k=1..oo} 1/sqrt(k).
0
3, 7, 22, 76, 280, 1071, 4190, 16571, 65910, 262892, 1050072, 4197295, 16783198, 67120828, 268459383, 1073789677, 4295063002, 17180060596, 68719859560, 274878672591, 1099513159069, 4398049573690, 17592192169587, 70368756428006, 281475001211340
OFFSET
1,1
COMMENTS
See Schechter, 1984, for precise definition. The sum-critical values for Sum 1/k begin 4, 31, 1674, ..., which is almost but not quite the same as A082913 (the latter has an additional 2 at the start).
LINKS
Murray Schechter, Summation of divergent series by computer, Amer. Math. Monthly, 91:10 (1984), 629-632. See Table 2.
FORMULA
a(n) ~ 2^(2*n - 2) - 2^(n-1)*zeta(1/2). - Vaclav Kotesovec, Jun 25 2022
MATHEMATICA
Table[Floor[x /. FindRoot[2*Sqrt[x] + (1 - 1/(12*x))/(2*Sqrt[x]) + Zeta[1/2] == 2^k, {x, 2^k}]] + 1, {k, 1, 25}] (* Vaclav Kotesovec, Jun 25 2022 *)
CROSSREFS
Cf. A082913.
Sequence in context: A259809 A340022 A181769 * A075214 A360887 A070766
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 24 2022
EXTENSIONS
More terms from Vaclav Kotesovec, Jun 25 2022
STATUS
approved