A354771 Sum-critical values for the divergent series Sum_{k=1..oo} 1/sqrt(k).

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

Table of n, a(n) for n=1..25.

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

Adjacent sequences: A354768 A354769 A354770 * A354772 A354773 A354774

Keyword

nonn

Author

N. J. A. Sloane, Jun 24 2022

Extensions

More terms from Vaclav Kotesovec, Jun 25 2022

Status

approved