|
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| 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.
|
|
|
LINKS
| Eric Weisstein's World of Mathematics, Prime Constellation
|
|
|
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
| A020497, A094660, A135311, Also compare A014657 which is unrelated but remarkably similar
Sequence in context: A141231 A047623 A190523 * A007950 A034936 A204657
Adjacent sequences: A161778 A161779 A161780 * A161782 A161783 A161784
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Carl R. White (oeisfan(AT)phodd.net), Jun 19 2009
|
| |
|
|
