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Members of the difference sequence (A091381) of the sequence of largest quadratic "mixed" residues modulo the primes (A091380) where the latter is non-monotonic.
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%I #9 Mar 14 2018 03:51:25

%S 0,-1,-5,-1,-3,0,0,-8,0,-1,0,-7,-2,-6,-1,0,0,-5,-6,0,0,-7,-2,0,-2,-3,

%T -1,0,-1,-5,-5,-7,-2,-11,0,-1,0,0,-1,-2,-10,0,0,-6,-3,-1,-5,-5,-6,-5,

%U 0,-1,-5,-7,-2,-5,-1,-5,0,-2,-2,-7,0,-7,-9,-4,-4,-8,-5,-13,0,-4,-4,-7,-17,0,-3,0,-5,-1,-3,0,-17,0,-7,-6,-1,-2,-3,-3,0

%N Members of the difference sequence (A091381) of the sequence of largest quadratic "mixed" residues modulo the primes (A091380) where the latter is non-monotonic.

%C The negative values are either primes or composites (Cf. A088200).

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

%o (PARI) {/* The difference sequence values where the sequence of the largest "mixed" QR modulo the primes is non-monotonic */ lqxr_nm_d(to)=local(v=[],k,r,q,p,e=1,n=0,i=1); while(n<to,i+=1;p=prime(i);k=p-1;r=p%4-2; while(kronecker(k,p)<>r,k-=1); if(k-e<=0,v=concat(v,k-e);n+=1);e=k); print(i);print(v) }

%Y Cf. A091380, A091381, A091382, A091383, A091385, A088190, A088196, A088200.

%K easy,sign

%O 1,3

%A Ferenc Adorjan (fadorjan(AT)freemail.hu)