A281998 a(n) is the smallest prime p such that there is a multiplicative subgroup H of Z/pZ, of even size and of index n, such that for any two cosets H1 and H2 of H, H1 + H2 contains all of (Z/pZ)\0.

3, 13, 19, 73, 131, 181, 197, 193, 379, 521, 397, 601, 1093, 1093, 1231, 1153, 1871, 1297, 2243, 1801, 2269, 2861, 3037, 3313, 4001, 4993, 3673, 5209, 5743, 4621, 5333, 4481, 6733, 8161, 9241, 9001, 9029, 7069, 8737, 9601

Offset

1,1

Comments

It must be that p = a(n) is equivalent to 1 mod 2n. The fact that H is of even size means H = -H. The finite integral relation algebra with n symmetric flexible diversity atoms is representable over Z/pZ, where p = a(n).

Links

Jeremy F. Alm, Table of n, a(n) for n = 1..1000

Jeremy F. Alm, Plot of a(n) on n

Crossrefs

Cf. A282001

Sequence in context: A007697 A055202 A158016 * A294676 A293465 A353251

Adjacent sequences: A281995 A281996 A281997 * A281999 A282000 A282001

Keyword

nonn

Author

Jeremy F. Alm, Feb 04 2017

Status

approved