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

2, 3, 37, 71, 73, 107, 109, 179, 211, 281, 283, 317, 353, 389, 421, 457, 491, 563, 599, 631, 701, 739, 773, 809, 877, 911, 947, 983, 1019, 1051, 1087, 1123, 1193, 1229, 1297, 1367, 1439, 1471, 1543, 1579, 1613, 1753, 1787, 1789, 1823, 1997, 1999, 2069, 2137

Offset

1,1

Comments

Or primes p such that p (mod 35) = {1, 2, 3, 4}.

In general if 0 < m (mod p) = m (mod q) then m (mod p*q) < p (with p < q any primes).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

37 = 2 (mod 5) = 2 (mod 7);
71 = 1 (mod 5) = 1 (mod 7);
73 = 3 (mod 5) = 3 (mod 7);
109 = 4 (mod 5) = 4 (mod 7).

Maple

select(isprime, [seq(seq(35*i+j, j=1..4), i=0..1000)]); # Robert Israel, Jan 18 2016

Mathematica

Select[Prime[Range[100]], Mod[#, 5]==Mod[#, 7]&]
Select[Prime[Range[100]], Mod[#, 35]<5&]

Prog

(Magma) [p: p in PrimesUpTo(2500) | p mod 5 eq p mod 7]; // Vincenzo Librandi, Jan 17 2016
(PARI) isok(n) = isprime(n) && ((n % 5) == (n % 7)); \\ Michel Marcus, Jan 17 2016
(PARI) lista(nn) = forprime(p=2, nn, if(p%5 == p%7, print1(p, ", "))); \\ Altug Alkan, Jan 18 2016

Crossrefs

Sequence in context: A340845 A266758 A280539 * A109748 A062459 A258455

Adjacent sequences: A216142 A216143 A216144 * A216146 A216147 A216148

Keyword

nonn,easy

Author

Zak Seidov, Sep 02 2012

Status

approved