A054643 Primes prime(n) such that prime(n) + prime(n+1) + prime(n+2) == 0 (mod 3).

3, 47, 151, 167, 199, 251, 257, 367, 503, 523, 557, 587, 601, 647, 727, 941, 971, 991, 1063, 1097, 1117, 1181, 1217, 1231, 1361, 1453, 1493, 1499, 1531, 1741, 1747, 1753, 1759, 1889, 1901, 1907, 2063, 2161, 2281, 2393, 2399, 2411, 2441, 2671, 2897, 2957

Offset: 1

Author

Labos Elemer, May 15 2000

Keywords

• nonn

Comments

The 2 differences of these 3 primes should be congruent of 6, except the first prime 3, for which 3 + 5 + 7 = 15 holds. Sequences like A047948, A052198 etc. are subsequences here.

Examples

			For prime(242) = 1531, the sum is 4623, the mean is 1541 and the successive differences are 6a=12 or 6b=6 resp.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A034961, A034707, A024675, A052288, A047948, A052198.

A122535 is a subsequence.

Cf. A075541 (for their indices).

Programs

Mathematica

Select[Partition[Prime@ Range@ 430, 3, 1], Divisible[Total@ #, 3] &][[All, 1]] (* Michael De Vlieger, Jun 29 2017 *)