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A321510 Primes p for which there exists a prime q < p such that 3*q == 1 (mod p). 1
5, 7, 19, 43, 61, 79, 109, 151, 163, 223, 271, 349, 421, 439, 523, 601, 613, 631, 673, 691, 811, 853, 919, 991, 1009, 1051, 1063, 1153, 1213, 1231, 1279, 1321, 1429, 1531, 1549, 1663, 1693, 1789, 1801, 1873, 1933, 1951, 2113, 2143, 2179, 2221, 2239, 2503, 2539, 2683, 2791, 2833, 2851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A104163 with 5 prepended (see example). For any prime p in A104163 q = (2*p+1)/3, then q < p and 3*q == 1 (mod p).

LINKS

Table of n, a(n) for n=1..53.

FORMULA

a(n+1) = A104163(n); n >= 1.

EXAMPLE

For p = 11, the only number t < 11 such that 3*t == 1 (mod 11) is t = 4, which is not prime, therefore 11 is not a term.

For p = 5, q = 2 (prime); 2*3 = 6 == 1 (mod 5) therefore 5 is a term.

MAPLE

for n from 3 to 300 do

Y := ithprime(n);

Z := 1/3 mod Y;

if isprime(Z) then print(Y);

end if:

end do:

MATHEMATICA

aQ[p_]:=Module[{ans=False, q=2}, While[q<p, If[Mod[3*q, p]==1, ans=True; Break[]]; q=NextPrime[q]]; ans]; Select[Prime[Range[350]], aQ] (* Amiram Eldar, Nov 12 2018 *)

Join[{5}, Select[Prime[Range[400]], PrimeQ[((2 # + 1)) / 3] &]] (* Vincenzo Librandi, Nov 17 2018 *)

PROG

(PARI) isok(p) = if (isprime(p), forprime(q=1, p-1, if ((3*q % p) == 1, return (1)))); \\ Michel Marcus, Nov 14 2018

CROSSREFS

Cf. A104163 (essentially the same sequence), A005383.

Sequence in context: A146470 A296935 A106987 * A084198 A036061 A288608

Adjacent sequences:  A321507 A321508 A321509 * A321511 A321512 A321513

KEYWORD

nonn

AUTHOR

David James Sycamore, Nov 11 2018

STATUS

approved

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Last modified August 24 14:11 EDT 2019. Contains 326282 sequences. (Running on oeis4.)