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

1,2

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.

Prog

(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))

Crossrefs

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

Cf. A304242, A304239, A304240.

Sequence in context: A044282 A044663 A142228 * A204735 A254283 A010019

Adjacent sequences: A304238 A304239 A304240 * A304242 A304243 A304244

Keyword

nonn,hard

Author

M. F. Hasler, May 08 2018

Extensions

More terms from Bert Dobbelaere, Oct 30 2018

Status

approved