A304241 Indices where Mertens function A002321 reaches record amplitudes between zeros.

1, 31, 114, 199, 443, 665, 1109, 1637, 2803, 7021, 8511, 9861, 19291, 24185, 31990, 42961, 48433, 59577, 96014, 141869, 230399, 300551, 355733, 603151, 926265, 1066854, 1793918, 3239797, 5343761, 6481601, 7109110, 10194458, 12874814, 30919091, 61913863

Offset: 1

Author

M. F. Hasler, May 08 2018

Keywords

• nonn
• hard

Comments

A subsequence of A051402 and A304239.

These are the indices where the Mertens function M = A002321 not only reaches a record value (in absolute value), but also its largest amplitude between subsequent zeros (as to avoid many "intermediate" records).

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..65
• Bert Dobbelaere, C++ program for A304241 and A304242
• G. Hurst, Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture, arXiv:1610.08551 [math.NT], 2016-2017.

Crossrefs

Cf. A002321, A028442 (zeros of M), A051400, A051401, A051402 (where M, -M, |M| reaches k = 1, 2, 3, ...).

Cf. A304242, A304239, A304240.

Programs

PARI

L=M=0;for(n=1,oo,if(m=A002321(n),abs(m)>abs(M)&&[M,N]=[m,n],abs(M)>abs(L) && (L=M) && print1(N",");M=0))

Extensions

More terms from Bert Dobbelaere, Oct 30 2018