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

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, 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, 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

Offset

2,2

Comments

The members of the sequence are either 1's or primes (easily provable).

Links

Table of n, a(n) for n=2..100.

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

Formula

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.

Mathematica

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 *)

Prog

(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)}

Crossrefs

Cf. A088192, A088196, A088197, A088199, A088200, A088201.

Sequence in context: A334029 A334297 A333765 * A318288 A088426 A124769

Adjacent sequences: A088195 A088196 A088197 * A088199 A088200 A088201

Keyword

easy,nonn

Author

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

Status

approved