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A072564
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Numbers m such that the absolute values of the real and imaginary part of zeta(1/2 + m*i) are both < 1.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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]
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LINKS
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EXAMPLE
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zeta(1/2 + 15*i) = (0.1471...) + (0.7047...)*i; 0.1471... < 1 and 0.7047... < 1, hence 15 is in the sequence.
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MATHEMATICA
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Select[Range[100], Abs[Re[Zeta[1/2 + #*I]]] < 1 && Abs[Im[Zeta[1/2 + #*I]]] < 1 &] (* Vaclav Kotesovec, Feb 18 2021 *)
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PROG
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(PARI) isok(m) = my(x=zeta(1/2+m*I)); (abs(real(x)) < 1) && (abs(imag(x)) < 1); \\ Michel Marcus, Feb 18 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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