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A123172
Least prime p for which Mertens's function M(p) = n.
0
13, 5, 3, 2, 97, 229, 223, 557, 569, 587, 1367, 1399, 1409, 2221, 1423, 2657, 3229, 3389, 3253, 3251, 3271, 3323, 3301, 3299, 8353, 8161, 8641, 8423, 8419, 8627, 11839, 8501, 8599, 8537, 8597, 8573, 8521, 8513, 11821, 11813, 19429, 19001, 11783, 11801, 11777
OFFSET
-3,1
FORMULA
a(n) = min{p in A000040 and A002321(p) = n}.
EXAMPLE
a(-3) = 13 = the first prime for which the Mertens function M(n) = -3.
a(-2) = 5 = the first prime for which the Mertens function M(n) = -2.
a(-1) = 3 = the first prime for which the Mertens function M(n) = -1.
a(0) = 2 = min{A000040 INTERSECTION A028442} = the first prime for which the Mertens function M(n) = 0.
a(1) = 97 = min{A000040 INTERSECTION A118684} = the first prime for which the Mertens function M(n) = 1.
a(2) = 229 = the first prime for which the Mertens function M(n) = 2.
a(3) = 223 = the first prime for which the Mertens function M(n) = 3.
PROG
(PARI) mertens(n) = sum( k=1, n, moebius(k)); \\ A002321
a(n) = {p = 2; while (mertens(p) != n, p = nextprime(p+1)); p; } \\ Michel Marcus, Sep 24 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Oct 02 2006
EXTENSIONS
More terms from Michel Marcus, Sep 24 2013
STATUS
approved