cp's OEIS Frontend

A267540 Primes p such that p (mod 3) = p (mod 5).

%I A267540 #37 Sep 08 2022 08:46:15
%S A267540 2,17,31,47,61,107,137,151,167,181,197,211,227,241,257,271,317,331,
%T A267540 347,421,467,541,557,571,587,601,617,631,647,661,677,691,751,797,811,
%U A267540 827,857,887,947,977,991,1021,1051,1097,1171,1187,1201,1217,1231,1277,1291
%N A267540 Primes p such that p (mod 3) = p (mod 5).
%C A267540 Or primes p such that p (mod 15) = {1, 2}.
%C A267540 Terminal digits in a(7)...a(32) alternate 26 times (7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1). 25 differences between the 2 consecutive terms in this range show patterns as well.
%C A267540 A differenceroot function can generate the terms a(7)...a(32).
%F A267540 a(n) = 1/2*((-1)^n*(3*(-1)^n*(10n+81)-1)) with (1<n<10) for a(7)...a(16).
%F A267540 G.f.: (x*(-14x^6-32x^5+16x^4+30x^3-x+14)+17)/((x-1)^2*(x+1)) generates a(2)...a(16), (0<=x<15).
%F A267540 G.f.: (x*(x*(30x*(-2x^4-x^3+x+2)-301)+14)+317)/((x-1)^2*(x+1)) generates a(17)...a(32), (0<=x<16).
%p A267540 select(isprime, [seq(seq(15*i+j, j= 1..2), i=0..10000)]); # _Robert Israel_, Jan 17 2016
%t A267540 Select[ Prime[ Range[10000]], (Mod[#,3] == Mod[#,5]) &] (* Or *)
%t A267540 Select[ Prime[ Range[10000]], 0 < Mod[#,15] < 3 &]
%o A267540 (Magma) [p: p in PrimesUpTo(2000) | p mod 3 eq p mod 5]; // _Vincenzo Librandi_, Jan 17 2016
%o A267540 (PARI) lista(nn) = forprime(p=2, nn, if(p%3 == p%5, print1(p, ", "))); \\ _Altug Alkan_, Jan 17 2016
%Y A267540 Cf. A063118, A141860, A216145.
%K A267540 nonn,easy
%O A267540 1,1
%A A267540 _Mikk Heidemaa_, Jan 16 2016
%E A267540 More terms from _Vincenzo Librandi_, Jan 17 2016