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A088198 Distance LQnR(p_n) (A088196) from p_n.

%I A088198 #20 Jun 08 2022 23:23:14
%S A088198 1,2,1,1,2,3,1,1,2,1,2,3,1,1,2,1,2,1,1,5,1,1,3,5,2,1,1,2,3,1,1,3,1,2,
%T A088198 1,2,1,1,2,1,2,1,5,2,1,1,1,1,2,3,1,7,1,3,1,2,1,2,3,1,2,1,1,5,2,1,5,1,
%U A088198 2,3,1,1,2,1,1,2,2,3,7,1,2,1,5,1,1,3,5,2,1,1,1,1,1,1,1,2,3,1,2
%N A088198 Distance LQnR(p_n) (A088196) from p_n.
%C A088198 The members of the sequence are either 1's or primes (easily provable).
%H A088198 Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/qrp.pdf">The sequence of largest quadratic residues modulo the primes</a>.
%F A088198 a(n) = prime(n)-LQnR(prime(n)) = A000040(n)-A088196(n), where prime(n) is the n-th prime and LQnR(m) is the largest quadratic non-residue modulo m.
%t A088198 qrQ[n_, p_] := Length[ Select[ Table[x^2, {x, 1, Floor[p/2]}], Mod[#, p] == n & , 1]] == 1; LQnR[p_] := Catch[ Do[ If[ !qrQ[k, p], Throw[k]], {k, p-1, 0, -1}]]; a[n_] := (p = Prime[n]; p - LQnR[p]); Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, May 14 2012 *)
%o A088198 (PARI) qnrp_pm(fr,n)= {/* The distance of primes from 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,p-m)); print(v)}
%Y A088198 Cf. A088192, A088196, A088197, A088199, A088200, A088201.
%K A088198 easy,nonn
%O A088198 2,2
%A A088198 Ferenc Adorjan (fadorjan(AT)freemail.hu), Sep 23 2003