A123172 Least prime p for which Mertens's function M(p) = n.

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

Links

Table of n, a(n) for n=-3..41.

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.

Mathematica

Mf=Accumulate[Array[MoebiusMu, 20000]] (* increase range for Mf for n>49 *); Table[i=0; Until[Mf[[Prime[i]]]==n, i++]; Prime[i], {n, -3, 49}] (* James C. McMahon, Nov 16 2024 *)

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

Cf. A000040, A002321, A028442, A118684.

Sequence in context: A222165 A277125 A249267 * A010218 A107833 A248146

Adjacent sequences: A123169 A123170 A123171 * A123173 A123174 A123175

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, Oct 02 2006

Extensions

More terms from Michel Marcus, Sep 24 2013

Status

approved