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A054643 Primes prime(n) such that prime(n) + prime(n+1) + prime(n+2) == 0 (mod 3). 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

A122535 is a subsequence.

Cf. A075541 (for their indices).

Sequence in context: A084295 A141850 A003551 * A122535 A058427 A142293

Adjacent sequences:  A054640 A054641 A054642 * A054644 A054645 A054646

KEYWORD

nonn

AUTHOR

Labos Elemer, May 15 2000

STATUS

approved

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Last modified July 4 11:45 EDT 2020. Contains 335448 sequences. (Running on oeis4.)