A091382 Distance between the sequence of primes and the largest "mixed" quadratic residues modulo the primes (A091380).

1, 2, 2, 3, 2, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 2, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 7, 5, 2, 3, 2, 3, 2, 2, 3, 7, 7, 2, 3, 5, 2, 3, 2, 3, 2, 2, 2, 11, 5, 2, 2, 5, 2, 2, 3, 7, 3, 2, 2, 5, 2, 2, 3, 7, 2, 2, 7, 5, 3, 2, 3, 5, 2, 3, 2, 13, 3, 2, 2, 5, 2, 3, 2, 2

Offset: 1

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu)

Keywords

• easy
• nonn

Comments

Apart from the first term, it contains solely primes. Is every prime in there?

Apart from the first term and the definition, it is identical to the sequence A053760 by S. R. Finch.

Links

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

Crossrefs

Cf. A091380, A091381, A091383, A091384, A091385, A088192, A088198.

Programs

PARI

{/* Distance of primes from the sequence of the largest "mixed" QR modulo the primes */ p_lqxr(to)=local(v=[1],k,r,q,p); for(i=2,to,p=prime(i);k=p-1;r=p%4-2; while(kronecker(k,p)<>r,k-=1); v=concat(v,p-k)); print(v) }