A390228 - OEIS

%I #13 Jan 20 2026 22:33:53

%S 1,8,9,16,17,23,23,67,67,67,67,67,79,101,101,113,127,127,127,127,127,

%T 211,233,283,293,367,367,367,367,367,373,563,563,563,563,563,563,563,

%U 563,563,563,677,677,677,677,677,677,677,677,677,677,677,677,677,677,677,677,773,773,773

%N Least positive integer m such that the n numbers c(0),...,c(n-1) are incongruent modulo m, where c(k) = A000521(k).

%C Conjecture: a(n) is prime for each n > 4.

%H Zhi-Wei Sun, <a href="/A390228/b390228.txt">Table of n, a(n) for n = 1..6520</a>

%H Zhi-Wei Sun, <a href="https://doi.org/10.1016/j.jnt.2013.02.003">On functions taking only prime values</a>, J. Number Theory, 133 (2013), no. 8, 2794-2812.

%e a(2) = 8 since c(1)*(c(1)-1) - c(0)*(c(0)-1) = 196884*196883 - 744*743 = 2^2*3*5*7*229*467*863 is not divisible by 8.

%t c[n_]:=c[n]=SeriesCoefficient[12^3 KleinInvariantJ[Log[q]/(2 Pi I)], {q, 0, n}];

%t f[n_]:=f[n]=c[n](c[n]-1);

%t tab={};m=1;Do[Label[bb]; If[Length[Union[Table[Mod[f[k], m], {k, 0, n-1}]]]==n,tab=Append[tab,m]; Goto[aa]]; m=m+1; Goto[bb]; Label[aa], {n, 1, 60}];Print[tab]

%Y Cf. A000040, A000521, A392667.

%K nonn

%O 1,2

%A _Zhi-Wei Sun_, Jan 20 2026