A096635 -id:A096635 - cp's OEIS frontend

A096634 Let p = n-th prime == 5 (mod 8) (A007521); a(n) = smallest prime q such that p is not a square mod q.

3, 5, 3, 5, 3, 7, 3, 11, 3, 5, 3, 7, 3, 7, 3, 5, 3, 3, 7, 5, 3, 5, 13, 3, 3, 11, 3, 5, 3, 7, 3, 3, 13, 5, 5, 3, 3, 3, 7, 5, 5, 3, 5, 3, 7, 3, 7, 5, 3, 5, 3, 5, 3, 5, 3, 3, 3, 11, 11, 5, 3, 13, 5, 3, 17, 3, 7, 5, 3, 3, 7, 11, 7, 3, 3, 5, 3, 3, 3, 7, 5, 3, 3, 3, 11, 3, 13, 5, 3, 3, 7, 3, 3, 11, 5, 3, 3, 5, 3

Offset: 1

Robert G. Wilson v, Jun 24 2004

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A094928, A096633, A096635, A096638.

g:= proc(n) local p;
  p:= 1;
  do
    p:= nextprime(p);
    if numtheory:-quadres(n,p) = -1 then return p fi
  od
end proc:
map(g, select(isprime, [seq(i,i=5..10000,8)])); # Robert Israel, Apr 17 2023

f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; f /@ Select[ Prime[ Range[435]], Mod[ #, 8] == 5 &]

A094929 Let p = n-th prime; a(n) = smallest odd prime q such that p is not a square mod q.

Original entry on oeis.org

3, 5, 3, 5, 3, 7, 3, 3, 7, 5, 3, 5, 3, 3, 3, 7, 5, 3, 5, 11, 3, 3, 5, 3, 5, 3, 11, 3, 5, 3, 3, 7, 3, 11, 5, 5, 3, 3, 3, 7, 3, 5, 3, 7, 11, 5, 3, 7, 3, 3, 7, 3, 3, 3, 3, 7, 5, 3, 5, 3, 5, 3, 5, 3, 13, 5, 3, 7, 3, 3, 5, 5, 13, 3, 3, 5, 3, 7, 3, 13, 3, 5, 7, 3, 3, 5, 3, 5, 3, 3, 5, 3, 13, 3, 3, 3, 5, 11, 5

Offset: 3

N. J. A. Sloane, Jun 19 2004

nonn

Cf. A094928, A096633, A096634, A096635.

f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; f /@ Prime[Range[3, 100]] (* Robert G. Wilson v, Jun 24 2004 *)

a(n) = {my(p=prime(n), q=3); while (!issquare(Mod(p, q)), q = nextprime(q+1)); q;} \\ Michel Marcus, May 06 2019

A096640 Smallest prime p == 7 mod 8 (A007521) and p > prime(n+2) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1), and p is a quadratic non-residue mod prime(n+2).

Original entry on oeis.org

23, 7, 31, 79, 631, 751, 2311, 21319, 48799, 82471, 256279, 78439, 1768831, 1365079, 2631511, 1427911, 4355311, 5715319, 49196359, 117678031, 180628639, 475477759, 452980999

Offset: 0

Robert G. Wilson v, Jun 24 2004

nonn

Same as smallest prime p == 7 mod 8 with the property that the Legendre symbol (p|q) = 1 for the first n odd primes q = prime(k+1), k = 1, 2, ..., n, and (p|q) = -1 for q = prime(n+2).

Cf. A096635, A096636.

f[n_] := Block[{k = 2}, While[ JacobiSymbol[n, Prime[k]] == 1, k++ ]; Prime[k]]; t = Table[0, {50}]; Do[p = Prime[n]; If[Mod[p, 8] == 7, a = f[p]; If[ t[[ PrimePi[a]]] == 0, t[[ PrimePi[a]]] = p; Print[ PrimePi[a], " = ", p]]], {n, 10^9}]; t

Better name from Jonathan Sondow, Mar 07 2013

cp's OEIS Frontend

A096634 Let p = n-th prime == 5 (mod 8) (A007521); a(n) = smallest prime q such that p is not a square mod q.

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A094929 Let p = n-th prime; a(n) = smallest odd prime q such that p is not a square mod q.

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A096640 Smallest prime p == 7 mod 8 (A007521) and p > prime(n+2) such that p is a quadratic residue mod the first n odd primes 3, 5, 7, 11, ..., prime(n+1), and p is a quadratic non-residue mod prime(n+2).

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