

A161781


Binary encodings of prime constellations.


0



1, 3, 5, 9, 11, 13, 17, 19, 25, 27, 33, 37, 41, 45, 65, 67, 69, 73, 75, 77, 81, 83, 89, 91, 97, 101, 105, 109, 129, 131, 137, 139, 145, 147, 153, 193, 195, 201, 203, 209, 211, 257, 261, 265, 269, 289, 293, 297, 301, 321, 325, 329, 333, 353, 357, 361, 365, 513, 515
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OFFSET

0,2


COMMENTS

Each constellation is encoded by means of dividing each of the increments to p in the ktuple 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.


LINKS



EXAMPLE

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).


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



