A088196 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

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

LINKS

Table of n, a(n) for n=2..60.

Chris Caldwell: The Prime Pages Quadratic Residues.

F. Adorjan, The sequence of largest quadratic residues modulo the primes.

PROG

(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)}

CROSSREFS

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

Sequence in context: A225175 A286954 A047402 * A112925 A193246 A239012

Adjacent sequences: A088193 A088194 A088195 * A088197 A088198 A088199

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved