A065742 Primes p(m) such that the set of quadratic residues modulo[p(m)] contains p(m-1).

17, 19, 29, 41, 43, 53, 59, 73, 79, 97, 101, 113, 127, 139, 173, 179, 193, 197, 211, 223, 233, 241, 251, 269, 281, 283, 293, 307, 313, 317, 337, 353, 389, 401, 409, 419, 433, 439, 457, 461, 499, 509, 523, 557, 563, 571, 577, 601, 607, 617, 619, 631, 641, 643

Offset

1,1

Links

Table of n, a(n) for n=1..54.

Example

Quadratic residue of modulus=17=p(4): {1,4,9,16,8,2,15,13,13,15,2,8,16,9,4,1,0} includes p(3)=13, the previous prime, so 17 is entered; Q.residue-set of 11,{1,4,9,5,3,3,5,9,4,1,0} does not include 7, thus 7 is not here.

Mathematica

t=Table[Count[Union[Table[Mod[w^2, Prime[k]], {w, 1, Prime[k]}]], Prime[k-1]], {k, 1, 180}]; Prime[Flatten[Position[t, 1]]]

Crossrefs

Sequence in context: A125213 A132246 A038969 * A155089 A101396 A050266

Adjacent sequences: A065739 A065740 A065741 * A065743 A065744 A065745

Keyword

nonn

Author

Labos Elemer, Nov 15 2001

Status

approved