A180217 a(n) = (n-th prime modulo 3) + (n-th prime modulo 4).

4, 3, 3, 4, 5, 2, 3, 4, 5, 3, 4, 2, 3, 4, 5, 3, 5, 2, 4, 5, 2, 4, 5, 3, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 3, 4, 2, 4, 5, 3, 5, 2, 5, 2, 3, 4, 4, 4, 5, 2, 3, 5, 2, 5, 3, 5, 3, 4, 2, 3, 4, 3, 4, 5, 2, 3, 4, 2, 5, 2, 3, 5, 4, 2, 4, 5, 3, 2, 3, 2, 5, 2, 5, 2, 4, 5, 3, 2, 3, 4, 5, 5, 4, 5, 4, 5, 3, 3, 4, 2, 4, 3

Offset: 1

Author

Zak Seidov, Jan 16 2011

Keywords

• nonn

Comments

a(n) = 2 iff prime(n) == 1 (mod 12); a(n) = 2 for prime(n) = 13, 37, 61, 73, 97, 109, ... (A068228).

a(n) = 5 iff prime(n) == 11 (mod 12); a(n) = 5 for prime(n) = 11, 23, 47, 59, 71, 83, ... (A068231).

For n > 2, a(n) = 3 iff prime(n) == 5 (mod 12); a(n) = 3 for prime(n) = 5, 17, 29, 41, 53, 89, ... (A040117).

For n > 2, a(n) = 4 iff prime(n) == 7 (mod 12); a(n) = 4 for prime(n) = 7, 19, 31, 43, 67, 79, ... (A068229).

Crossrefs

Equals A039701 + A039702.

Cf. A068228, A068231, A040117, A068229, A039710.

Programs

Magma

A180217:=func< n | p mod 3 + p mod 4 where p is NthPrime(n) >; [ A180217(n): n in [1..105] ]; // Klaus Brockhaus, Jan 18 2011

Mathematica

Mod[#,3]+Mod[#,4]&/@Prime[Range[110]] (* Harvey P. Dale, Nov 09 2011 *)