cp's OEIS Frontend

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

%I A088195 #5 Mar 14 2018 03:51:12
%S A088195 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,
%T A088195 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,
%U A088195 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
%N A088195 Distance (A088192) of primes from the largest quadratic residues modulo the primes (A088190), where the latter is non-monotonic.
%C A088195 The values are some odd primes, but never 5. The maximum value increases very slowly, it only reaches 31 for the first 20000 primes.
%C A088195 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.
%C A088195 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.
%H A088195 Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/qrp.pdf">The sequence of largest quadratic residues modulo the primes</a>.
%o A088195 (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) }
%Y A088195 Cf. A088190, A088191, A088192, A088193, A088194.
%K A088195 easy,nonn
%O A088195 1,1
%A A088195 Ferenc Adorjan (fadorjan(AT)freemail.hu), Sep 22 2003