A320774 Primes p for which there is a prime q < p such that 5*q == 1 (mod p).

3, 7, 17, 47, 107, 167, 197, 241, 257, 317, 347, 421, 541, 557, 571, 677, 751, 827, 947, 1097, 1171, 1217, 1291, 1307, 1367, 1427, 1607, 1621, 1847, 1861, 1877, 2011, 2027, 2207, 2221, 2251, 2267, 2297, 2341, 2417, 2477, 2521, 2657, 2671, 2851, 2927, 2971, 3257, 3271, 3361, 3391, 3541, 3557, 3571

Offset

1,1

Comments

All terms > a(1) are primes p such that either (2*p+1)/5 or (4*p+1)/5 is prime. A necessary (but not sufficient) condition for prime p > 3 to be a term is that its final digit must be 7 or 1 (otherwise (2*p+1), (4*p+1) respectively cannot be divisible by 5). The Maple code below computes terms > a(1).

Links

Table of n, a(n) for n=1..54.

Example

3 is a term since with q = 2 (prime < 3) we have 5*2 = 10 == 1 (mod 3).
7 is a term since with q = 3 (prime < 7) we have 5*q = 5*3 = 15 == 1 (mod 7).
241 is a term since with q = 193 (prime < 241) we have 5*193 = 965 == 1 (mod 241).

Maple

for n from 4 to 350 do
Y := ithprime(n);
Z := 1/5 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[5*q, p]==1, ans=True; Break[]]; q=NextPrime[q]]; ans]; Select[Prime[Range[350]], aQ] (* Amiram Eldar, Nov 12 2018 *)

Crossrefs

Cf. A005383, A104164, A321510, A321582.

Sequence in context: A062810 A113985 A309302 * A151265 A351437 A179944

Adjacent sequences: A320771 A320772 A320773 * A320775 A320776 A320777

Keyword

nonn

Author

David James Sycamore, Nov 12 2018

Status

approved