A267550 Primes p such that p (mod 3) = p (mod 5) = p (mod 7).

2, 107, 211, 317, 421, 631, 947, 1051, 1367, 1471, 1787, 1997, 2207, 2311, 2417, 2521, 2731, 2837, 3257, 3361, 3467, 3571, 3677, 4201, 4517, 4621, 4831, 4937, 5147, 5881, 5987, 6091, 6197, 6301, 6827, 7247, 7351, 7457, 7561, 7877, 8087, 8191, 8297, 8821, 9137, 9241, 9661, 9767, 9871, 10501

Offset: 1

Author

Mikk Heidemaa, Jan 17 2016

Keywords

• nonn
• easy

Comments

Or primes p such that p (mod 105) = {1, 2}.

In terms a(4227)...a(4246) their terminal digits alternate: 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A216145, A267540.

Programs

Magma

[p: p in PrimesUpTo(10000) | p mod 3 eq p mod 5 and p mod 5 eq p mod 7]; // Vincenzo Librandi, Jan 17 2016

Mathematica

Select[ Prime[ Range[10000]], (Mod[#,3] == Mod[#,5] == Mod[#,7]) &](*Or*)
Select[ Prime[ Range[10000]], 0 < Mod[#,105] < 3 &]
Select[Prime[Range[10000]],Length[Union[Mod[#,{3,5,7}]]]==1&] (* Harvey P. Dale, Oct 11 2019 *)

PARI

lista(nn) = forprime(p=2, nn, if(p%3 == p%5 && p%5 == p%7, print1(p, ", "))); \\ Altug Alkan, Jan 25 2016

Extensions

More terms from Vincenzo Librandi, Jan 17 2016