OFFSET
1,2
COMMENTS
Conjecture: a(n) is always positive. Moreover, a(n) <= 2*prime(n) for all n > 0.
Note that a(15) = 94 = 2*prime(15).
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..100
Zhi-Wei Sun, On a^n+bn modulo m, preprint, arXiv:1312.1166 [math.NT], 2013-2014.
EXAMPLE
a(4) = 8 since {A000720(4*k): k = 1, ..., 8} = {2, 4, 5, 6, 8, 9, 9, 11} contains a complete system of residues modulo 4, but {pi(4*k): k = 1, ..., 7} contains no integer congruent to 3 modulo 4.
MATHEMATICA
q[m_, n_]:=Length[Union[Table[Mod[PrimePi[k*n], n], {k, 1, m}]]]
Do[Do[If[q[m, n]==n, Print[n, " ", m]; Goto[aa]], {m, n, 2*Prime[n]}];
Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 60}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Feb 10 2014
STATUS
approved