A269704 -id:A269704 - cp's OEIS frontend

A094928 Let p = n-th prime == 1 mod 8 (A007519); a(n) = smallest prime q such that p is not a square mod q.

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

Offset: 1

N. J. A. Sloane, Jun 19 2004

			n=3, p = 73, a(3) = q = 5: Legendre(73,5) = -1.

M. Kneser, Quadratische Formen, Springer, 2002; see Hilfssatz 18.3.

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

Cf. A007519, A002224, A144294, A269704.

Subsequence of A094929.

f:= proc(p) local q;
     q:= 3:
     do
      if numtheory:-quadres(p,q) = -1 then return q fi;
      q:= nextprime(q);
     od;
end proc:
map(f, select(isprime, [seq(p,p=1..10000,8)])); # Robert Israel, May 06 2019

f[n_] := Prime[ Position[ JacobiSymbol[n, Select[Range[3, n - 1], PrimeQ[ # ] &]], -1][[1, 1]] + 1]; f /@ Select[ Prime[ Range[435]], Mod[ #, 8] == 1 &] (* Robert G. Wilson v, Jun 23 2004 *)

a(n) = A094929(A269704(n)). - Robert Israel, May 06 2019

More terms from Robert G. Wilson v, Jun 23 2004

A269703 Numbers k such that prime(k) == 1 (mod 7).

Original entry on oeis.org

10, 14, 20, 30, 31, 45, 47, 52, 60, 68, 75, 82, 87, 90, 94, 101, 113, 115, 120, 122, 126, 132, 134, 144, 153, 156, 162, 163, 169, 177, 183, 192, 209, 213, 220, 226, 233, 239, 250, 251, 262, 267, 269, 288, 295, 304, 306, 315, 320, 324, 330, 337, 342, 344, 346

Offset: 1

Vincenzo Librandi, Mar 04 2016

nonn

The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

			a(1) = 10 because prime(10) = 29 and 29 == 1 (mod 7).

The associated primes are in A004619.

Sequences of numbers n such that prime(n) == 1 (mod k): A091178 (k=3,6), A080147 (k=4), A049511 (k=5,10), this sequence (k=7), A269704 (k=8), A269705 (k=9).

[n: n in [1..500] | NthPrime(n) mod 7 eq 1];

Select[Range[500], Mod[Prime[#], 7] == 1 &]

lista(nn) = for(n=1, nn, if(Mod(prime(n),7)==1, print1(n, ", "))); \\ Altug Alkan, Mar 04 2016

a(n) ~ 6*n. - Charles R Greathouse IV, Sep 20 2016 [Corrected by Amiram Eldar, Mar 01 2021]

cp's OEIS Frontend

A094928 Let p = n-th prime == 1 mod 8 (A007519); a(n) = smallest prime q such that p is not a square mod q.

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