A088201 - OEIS

%I #8 Mar 17 2018 04:04:36

%S 5,5,7,5,5,7,5,11,5,11,7,7,7,5,7,5,5,13,5,7,11,7,7,11,13,5,7,11,7,5,

%T 11,7,7,5,7,7,7,13,7,7,11,7,5,5,11,7,7,7,13,13,17,5,11,11,17,11,7,7,

%U 13,5,7,7,13,7,5,7,7,5,5,13,5,7,11,13,7,7,17,11,5,7,11,11,7,11,7,7,5,7

%N Distance p_n-LQnR(p_n) (A088198) where the difference sequence (A088197) of LQnR(p_n) (A088196) is <= 0.

%C The terms are conjectured to be odd primes > 3.

%C It is also conjectured that the i-th member of A088200 is -2 if and only if a(i) is 5.

%C The terms are conjectured to be odd primes > 3 (the primality is provable).

%H Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/qrp.pdf">The sequence of largest quadratic residues modulo the primes</a>.

%o (PARI) qnrp_pm_nm(n)= {/* The distance of p from LQnR where the sequence of the largest QnR modulo the primes is nonmonotonic */ local(k=1,m,p,fl,jj,j,v=[]); for(i=2,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--); if(m-k<=0,v=concat(v,p-m)); k=m); print(v)}

%Y Cf. A088195, A088196, A088197, A088198, A088199, A088200.

%K nonn

%O 1,1

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