The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304242 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A304242

Increasingly larger (in absolute value) extrema of the Mertens function A002321 between subsequent zeros.
(history; published version)

#15 by Alois P. Heinz at Tue Oct 30 15:52:45 EDT 2018

STATUS

proposed

approved

#14 by Michel Marcus at Tue Oct 30 13:51:32 EDT 2018

STATUS

editing

proposed

#13 by Michel Marcus at Tue Oct 30 13:51:25 EDT 2018

LINKS

G. Hurst, <a href="https://arxiv.org/abs/1610.08551">Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture</a>

G. Hurst, <a href="https://arxiv.org/abs/1610.08551">Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture</a>, arXiv:1610.08551 [math.NT], 2016-2017.

STATUS

proposed

editing

#12 by Bert Dobbelaere at Tue Oct 30 13:32:18 EDT 2018

STATUS

editing

proposed

#11 by Bert Dobbelaere at Tue Oct 30 13:22:31 EDT 2018

LINKS

G. Hurst, <a href="https://arxiv.org/abs/1610.08551">Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture</a>

Bert Dobbelaere, <a href="/A304241/a304241.cpp.txt">C++ program for A304241 and A304242</a>

#10 by Bert Dobbelaere at Tue Oct 30 13:00:32 EDT 2018

DATA

1, -4, -6, -8, -9, -12, -15, -16, -25, -29, 35, -43, 51, -72, 73, -88, 96, -113, -132, -134, -154, 240, -258, -278, -368, 432, 550, -683, -847, 1060, -1078, 1240, -1447, -2573, 2845, -3448, -4610, -6226, 6695, -8565, 9132, 10246, -15335, -17334, 21777, -25071

LINKS

Bert Dobbelaere, <a href="/A304242/b304242.txt">Table of n, a(n) for n = 1..65</a>

KEYWORD

sign,hard,more

EXTENSIONS

More terms from Bert Dobbelaere, Oct 30 2018

STATUS

approved

editing

#9 by M. F. Hasler at Sun May 13 10:27:05 EDT 2018

STATUS

editing

approved

#8 by M. F. Hasler at Sun May 13 10:27:01 EDT 2018

NAME

Increasingly larger maxima, (in absolute value, ) extrema of the Mertens function A002321 between subsequent zeros.

PROG

(PARI) print1(j=1); for(i=1, #A051402-1, while( A028442[j] < A051402[i], j++); if( A028442[j-(j>1)]<=A051402[i] && A028442[j] < A051402[i+1], print1(", "A002321(A051402[i])))) \\ Using precomputed vectors A002321 and A051402, e.g. from the b-files: {c=0; AX=apply(t->fromdigits(digits(t)[#Str(c++)+1..-1]), readvec("/tmp/bX.txt"))}

STATUS

proposed

editing

#7 by M. F. Hasler at Tue May 08 20:36:12 EDT 2018

STATUS

editing

proposed

Discussion

Tue May 08

20:51

M. F. Hasler: (PARI) print1(j=1);for(i=1,#A051402-1,while( A028442[j] < A051402[i], j++); if( A028442[j-(j>1)]<=A051402[i] && A028442[j] < A051402[i+1], print1(","A002321(A051402[i]))))

#6 by M. F. Hasler at Tue May 08 20:28:40 EDT 2018

DATA

1, -4, -6, -8, -9, -12, -15, -16, -25, -29, 35, -43, 51, -72, 73, -88, 96, -113, -132, -134, -154, 240, -258, -278, -368, 432, 550, -683, -847

KEYWORD

sign,changedhard,more

STATUS

proposed

editing

Discussion

Tue May 08

20:36

M. F. Hasler: Now I have used the available list of 10 000 zeros of M, up to 5 631 198, and "inverse M" up to a value of +/- 1000, occurring at n = 6 447 543. The next value is either > +/- 1000, or the next larger root is beyond 5.6*10^6.