A216145 -id:A216145 - cp's OEIS frontend

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

Mikk Heidemaa, Jan 16 2016

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).

Cf. A063118, A141860, A216145.

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

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

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

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

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).

More terms from Vincenzo Librandi, Jan 17 2016

A267550 Primes p such that p (mod 3) = p (mod 5) = p (mod 7).

Original entry on oeis.org

2, 107, 211, 317, 421, 631, 947, 1051, 1367, 1471, 1787, 1997, 2207, 2311, 2417, 2521, 2731, 2837, 3257, 3361, 3467, 3571, 3677, 4201, 4517, 4621, 4831, 4937, 5147, 5881, 5987, 6091, 6197, 6301, 6827, 7247, 7351, 7457, 7561, 7877, 8087, 8191, 8297, 8821, 9137, 9241, 9661, 9767, 9871, 10501

Offset: 1

Mikk Heidemaa, Jan 17 2016

Or primes p such that p (mod 105) = {1, 2}.

In terms a(4227)...a(4246) their terminal digits alternate: 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7, 1, 7.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A216145, A267540.

[p: p in PrimesUpTo(10000) | p mod 3 eq p mod 5 and p mod 5 eq p mod 7]; // Vincenzo Librandi, Jan 17 2016

Select[ Prime[ Range[10000]], (Mod[#,3] == Mod[#,5] == Mod[#,7]) &](*Or*)
Select[ Prime[ Range[10000]], 0 < Mod[#,105] < 3 &]
Select[Prime[Range[10000]],Length[Union[Mod[#,{3,5,7}]]]==1&] (* Harvey P. Dale, Oct 11 2019 *)

lista(nn) = forprime(p=2, nn, if(p%3 == p%5 && p%5 == p%7, print1(p, ", "))); \\ Altug Alkan, Jan 25 2016

More terms from Vincenzo Librandi, Jan 17 2016

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cp's OEIS Frontend

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

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