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

Author

David James Sycamore, Nov 12 2018

Keywords

• nonn

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).

Examples

			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).
		

Crossrefs

Cf. A005383, A104164, A321510, A321582.

Programs

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[qAmiram Eldar, Nov 12 2018 *)