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A054643 Primes prime(n) such that prime(n) + prime(n+1) + prime(n+2) == 0 (mod 3). 19

%I #21 Jun 30 2017 03:03:13

%S 3,47,151,167,199,251,257,367,503,523,557,587,601,647,727,941,971,991,

%T 1063,1097,1117,1181,1217,1231,1361,1453,1493,1499,1531,1741,1747,

%U 1753,1759,1889,1901,1907,2063,2161,2281,2393,2399,2411,2441,2671,2897,2957

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

%C 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.

%H Zak Seidov, <a href="/A054643/b054643.txt">Table of n, a(n) for n = 1..1000</a>

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

%t Select[Partition[Prime@ Range@ 430, 3, 1], Divisible[Total@ #, 3] &][[All, 1]] (* _Michael De Vlieger_, Jun 29 2017 *)

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

%Y A122535 is a subsequence.

%Y Cf. A075541 (for their indices).

%K nonn

%O 1,1

%A _Labos Elemer_, May 15 2000

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)