A072564 Numbers m such that the absolute values of the real and imaginary part of zeta(1/2 + m*i) are both < 1.

1, 2, 3, 4, 5, 6, 13, 14, 15, 21, 22, 24, 25, 30, 31, 32, 33, 38, 41, 43, 48, 49, 50, 53, 57, 59, 60, 61, 65, 67, 69, 70, 72, 76, 77, 78, 79, 83, 84, 85, 87, 88, 89, 94, 95, 96, 99, 101, 104, 105, 106, 107, 111, 112, 114, 116, 119, 121, 122, 123, 124, 130, 131, 134, 135

Offset

1,2

Comments

Conjecture: lim_{n->infinity} a(n)/n = C exists, with 5 < C < 6. [The conjecture was based on erroneous terms; C is about 2.05 (see graph). - Vaclav Kotesovec, Feb 18 2021]

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Plot of a(n)/n for n = 1..10000

Example

zeta(1/2 + 15*i) = (0.1471...) + (0.7047...)*i; 0.1471... < 1 and 0.7047... < 1, hence 15 is in the sequence.

Mathematica

Select[Range[100], Abs[Re[Zeta[1/2 + #*I]]] < 1 && Abs[Im[Zeta[1/2 + #*I]]] < 1 &] (* Vaclav Kotesovec, Feb 18 2021 *)

Prog

(PARI) isok(m) = my(x=zeta(1/2+m*I)); (abs(real(x)) < 1) && (abs(imag(x)) < 1); \\ Michel Marcus, Feb 18 2021

Crossrefs

Sequence in context: A115307 A171597 A086185 * A223938 A222194 A057224

Adjacent sequences: A072561 A072562 A072563 * A072565 A072566 A072567

Keyword

nonn

Author

Benoit Cloitre, Aug 06 2002

Extensions

Corrected by Michel Marcus, Feb 18 2021

Status

approved