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Smallest k such that |M(k)| = 2^n, where M(x) is Mertens's function A002321.
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%I #29 May 06 2024 01:42:51

%S 1,5,31,199,1637,8507,24110,95961,355541,1786062,6473791,30649362,

%T 109851909,456774199,2589994747,7613644886,37725066313,108500046711

%N Smallest k such that |M(k)| = 2^n, where M(x) is Mertens's function A002321.

%D Karl Sabbagh, The Riemann Hypothesis, The Greatest Unsolved Problem in Mathematics, Farrar, Straus and Giroux, New York, 2002, page 191.

%F a(n) = A051402(2^n). - _Amiram Eldar_, May 06 2024

%t i = s = 0; Do[ While[ Abs[s] < 2^n, s = s + MoebiusMu[i]; i++ ]; Print[i - 1], {n, 0, 25}]

%Y Cf. A002321, A051402, A084234.

%K nonn,more

%O 1,2

%A _Robert G. Wilson v_, May 13 2003

%E Definition corrected by _L. Edson Jeffery_, Mar 18 2013

%E a(15)-a(18) by Ashley Jordan and _Luke March_, Jul 22 2014