|
Search: id:A084234
|
|
|
| A084234 |
|
Smallest k such that |M(k)| = n^2, where M(x) is Mertens's function A002321. |
|
+0
1
|
|
| 1, 31, 443, 1637, 2803, 9749, 19111, 24110, 42833, 59426, 95514, 230227, 297335, 297573, 299129, 355541, 897531, 924717, 926173, 1062397, 1761649, 1763079, 1789062, 3214693, 3218010, 3232958, 4962865, 5307549, 5343710, 6433477
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
"[I]f the absolute value of M(n) can be proved to be always less than the square root of n, then the Riemann Hypothesis is true. This is called Mertens's conjecture. ... Then along came Andrew Odlyzko and his colleague, Herman te Riele, and they showed in 1984 that there is a number, far larger than 10^30, that invalidates Mertens's conjecture - call it N. In other words, M(N) is greater than the square of N. So the conjecture is not true." [Sabbagh]
|
|
REFERENCES
|
Karl Sabbagh, The Riemann Hypothesis, The Greatest Unsolved Problem in Mathematics, Farrar, Straus and Giroux, New York, 2002, page 191.
|
|
MATHEMATICA
|
i = s = 0; Do[While[Abs[s] < n^2, s = s + MoebiusMu[i]; i++ ]; Print[i - 1], {n, 1, 25}]
|
|
CROSSREFS
|
Cf. A051402.
Sequence in context: A134071 A010836 A022723 this_sequence A118196 A125466 A142280
Adjacent sequences: A084231 A084232 A084233 this_sequence A084235 A084236 A084237
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), May 13 2003
|
|
|
Search completed in 0.002 seconds
|
