0,2

Each constellation is encoded by means of dividing each of the increments to p in the k-tuple by two, raising two to the power of each and then summing the result. e.g.:

. (p,p+2,p+6) -> p+(0,2,6) => (0,1,3) -> 2^0 + 2^1 + 2^3 = 11

Each encoding is unique and so can be reversed e.g.:

. 89 = 2^0 + 2^3 + 2^4 + 2^6 -> (0,3,4,6) => (p,p+6,p+8,p+12)

Those constellations that represent all moduli for all their matching primes p are not counted; For example, encoding #7, which implies (p,p+2,p+4) only matches the prime triple (3,5,7) which is (0,2,1) mod 3, and so is not a valid constellation, and thus 7 is not in the list. Encoding #155 is the first that fails modulo 5, and is also not in the list.

Mathworld Prime Constellation Page

Encoding #1 corresponds to the primes themselves (constellations of one), #3 corresponds to the twin primes (p,p+2), #5 to the cousin primes (p,p+4) and #9 to the 'sexy' primes (p,p+6).

A020497, A094660, A135311, Also compare A014657 which is unrelated but remarkably similar

Sequence in context: A162699 A141231 A047623 this_sequence A007950 A034936 A167791

Adjacent sequences: A161778 A161779 A161780 this_sequence A161782 A161783 A161784

nonn

Carl R. White (oeisfan(AT)phodd.net), Jun 19 2009