A088196 Largest number that is not a quadratic residue modulo prime(n).

2, 3, 6, 10, 11, 14, 18, 22, 27, 30, 35, 38, 42, 46, 51, 58, 59, 66, 70, 68, 78, 82, 86, 92, 99, 102, 106, 107, 110, 126, 130, 134, 138, 147, 150, 155, 162, 166, 171, 178, 179, 190, 188, 195, 198, 210, 222, 226, 227, 230, 238, 234, 250, 254, 262, 267, 270, 275, 278

Offset: 2

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Sep 23 2003

Keywords

• easy
• nonn

Comments

These are sometimes called quadratic non-residues modulo p(n). Denote a(n) by LQnR(p_n).

Links

• Chris Caldwell: The Prime Pages Quadratic Residues.
• F. Adorjan, The sequence of largest quadratic residues modulo the primes.

Crossrefs

Cf. A088190, A088197, A088198, A088199, A088200, A088201.

Programs

PARI

qnrp(fr,n)= {/* The largest QnR modulo the primes */ local(m,p,fl,jj,j,v=[]); fr=max(fr,2); for(i=fr,n,m=0; p=prime(i); jj=0; fl=2^p-1; j=2; while((j<=(p-1)/2),jj=(j^2)%p; fl-=2^jj; j++); j=p-1; while(m==0,if(bitand(2^j,fl),m=j); j--); v=concat(v,m)); print(v)}