A390228 Least positive integer m such that the n numbers c(0),...,c(n-1) are incongruent modulo m, where c(k) = A000521(k).

1, 8, 9, 16, 17, 23, 23, 67, 67, 67, 67, 67, 79, 101, 101, 113, 127, 127, 127, 127, 127, 211, 233, 283, 293, 367, 367, 367, 367, 367, 373, 563, 563, 563, 563, 563, 563, 563, 563, 563, 563, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 773, 773, 773

Offset

1,2

Comments

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

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..6520

Zhi-Wei Sun, On functions taking only prime values, J. Number Theory, 133 (2013), no. 8, 2794-2812.

Example

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.

Mathematica

c[n_]:=c[n]=SeriesCoefficient[12^3 KleinInvariantJ[Log[q]/(2 Pi I)], {q, 0, n}];
f[n_]:=f[n]=c[n](c[n]-1);
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]

Crossrefs

Cf. A000040, A000521, A392667.

Sequence in context: A265221 A286476 A265732 * A047393 A241263 A307417

Adjacent sequences: A390225 A390226 A390227 * A390229 A390230 A390231

Keyword

nonn

Author

Zhi-Wei Sun, Jan 20 2026

Status

approved