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A216145 Primes p such that p (mod 5) = p (mod 7).

%I A216145 #22 Sep 08 2022 08:46:03
%S A216145 2,3,37,71,73,107,109,179,211,281,283,317,353,389,421,457,491,563,599,
%T A216145 631,701,739,773,809,877,911,947,983,1019,1051,1087,1123,1193,1229,
%U A216145 1297,1367,1439,1471,1543,1579,1613,1753,1787,1789,1823,1997,1999,2069,2137
%N A216145 Primes p such that p (mod 5) = p (mod 7).
%C A216145 Or primes p such that p (mod 35) = {1, 2, 3, 4}.
%C A216145 In general if 0 < m (mod p) = m (mod q) then m (mod p*q) < p (with p < q any primes).
%H A216145 Robert Israel, <a href="/A216145/b216145.txt">Table of n, a(n) for n = 1..10000</a>
%e A216145 37 = 2 (mod 5) = 2 (mod 7);
%e A216145 71 = 1 (mod 5) = 1 (mod 7);
%e A216145 73 = 3 (mod 5) = 3 (mod 7);
%e A216145 109 = 4 (mod 5) = 4 (mod 7).
%p A216145 select(isprime, [seq(seq(35*i+j,j=1..4),i=0..1000)]); # _Robert Israel_, Jan 18 2016
%t A216145 Select[Prime[Range[100]],Mod[#,5]==Mod[#,7]&]
%t A216145 Select[Prime[Range[100]],Mod[#,35]<5&]
%o A216145 (Magma) [p: p in PrimesUpTo(2500) | p mod 5 eq p mod 7]; // _Vincenzo Librandi_, Jan 17 2016
%o A216145 (PARI) isok(n) = isprime(n) && ((n % 5) == (n % 7)); \\ _Michel Marcus_, Jan 17 2016
%o A216145 (PARI) lista(nn) = forprime(p=2, nn, if(p%5 == p%7, print1(p, ", "))); \\ _Altug Alkan_, Jan 18 2016
%K A216145 nonn,easy
%O A216145 1,1
%A A216145 _Zak Seidov_, Sep 02 2012