A088195 Distance (A088192) of primes from the largest quadratic residues modulo the primes (A088190), where the latter is non-monotonic.

3, 3, 3, 7, 3, 3, 3, 7, 3, 11, 7, 3, 7, 11, 3, 11, 7, 3, 3, 3, 3, 7, 17, 7, 3, 3, 3, 3, 3, 3, 13, 3, 11, 3, 7, 3, 11, 3, 3, 3, 3, 3, 13, 3, 11, 3, 3, 3, 3, 3, 11, 7, 11, 13, 3, 7, 7, 11, 7, 3, 3, 11, 19, 3, 11, 3, 3, 11, 17, 3, 11, 3, 7, 3, 13, 3, 3, 3, 3, 11, 11, 3, 3, 3, 3, 13, 19, 3, 3, 3, 7, 11

Offset

1,1

Comments

The values are some odd primes, but never 5. The maximum value increases very slowly, it only reaches 31 for the first 20000 primes.

It is conjectured that if we denote the members of A088194 by D(n) and the member of this sequence by M(n) then if D(n)=-1 then M(n)=7, while if M(n)=3 then D(n)=0.

The values are odd primes, but never 5 (the primality is provable). The maximum value increases very slowly: it only reaches 43 for the first 10^5 primes.

Links

Table of n, a(n) for n=1..92.

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

Prog

(PARI) qrp_pm_nm(to)= {/* The distance of LQR from the primes where the sequence of the largest QR modulo the primes is non-monotonic */ local(m, k=1, p, v=[]); for(i=2, to, m=1; p=prime(i); j=2; while((j<=(p-1)/2)&&(m<p-1), m=max(m, (j^2)%p); j++); if((m-k)<=0, v=concat(v, p-m)); k=m); print(v) }

Crossrefs

Cf. A088190, A088191, A088192, A088193, A088194.

Sequence in context: A212091 A061021 A126608 * A131757 A214834 A291767

Adjacent sequences: A088192 A088193 A088194 * A088196 A088197 A088198

Keyword

easy,nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Sep 22 2003

Status

approved