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

Author

Mikk Heidemaa, Jan 16 2016

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A063118, A141860, A216145.

Programs

Magma

[p: p in PrimesUpTo(2000) | p mod 3 eq p mod 5]; // Vincenzo Librandi, Jan 17 2016

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 &]

PARI

lista(nn) = forprime(p=2, nn, if(p%3 == p%5, print1(p, ", "))); \\ Altug Alkan, Jan 17 2016

Formula

a(n) = 1/2*((-1)^n*(3*(-1)^n*(10n+81)-1)) with (1

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).

Extensions

More terms from Vincenzo Librandi, Jan 17 2016

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