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

2, 17, 31, 47, 61, 107, 137, 151, 167, 181, 197, 211, 227, 241, 257, 271, 317, 331, 347, 421, 467, 541, 557, 571, 587, 601, 617, 631, 647, 661, 677, 691, 751, 797, 811, 827, 857, 887, 947, 977, 991, 1021, 1051, 1097, 1171, 1187, 1201, 1217, 1231, 1277, 1291

Offset

1,1

Comments

Or primes p such that p (mod 15) = {1, 2}.

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.

A differenceroot function can generate the terms a(7)...a(32).

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = 1/2*((-1)^n*(3*(-1)^n*(10n+81)-1)) with (1<n<10) for a(7)...a(16).

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).

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).

Maple

select(isprime, [seq(seq(15*i+j, j= 1..2), i=0..10000)]); # Robert Israel, Jan 17 2016

Mathematica

Select[ Prime[ Range[10000]], (Mod[#, 3] == Mod[#, 5]) &] (* Or *)
Select[ Prime[ Range[10000]], 0 < Mod[#, 15] < 3 &]

Prog

(Magma) [p: p in PrimesUpTo(2000) | p mod 3 eq p mod 5]; // Vincenzo Librandi, Jan 17 2016
(PARI) lista(nn) = forprime(p=2, nn, if(p%3 == p%5, print1(p, ", "))); \\ Altug Alkan, Jan 17 2016

Crossrefs

Cf. A063118, A141860, A216145.

Sequence in context: A362035 A197186 A063118 * A141068 A162622 A078164

Adjacent sequences: A267537 A267538 A267539 * A267541 A267542 A267543

Keyword

nonn,easy

Author

Mikk Heidemaa, Jan 16 2016

Extensions

More terms from Vincenzo Librandi, Jan 17 2016

Status

approved