This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A161781 #10 Feb 16 2025 08:33:10 %S A161781 1,3,5,9,11,13,17,19,25,27,33,37,41,45,65,67,69,73,75,77,81,83,89,91, %T A161781 97,101,105,109,129,131,137,139,145,147,153,193,195,201,203,209,211, %U A161781 257,261,265,269,289,293,297,301,321,325,329,333,353,357,361,365,513,515 %N A161781 Binary encodings of prime constellations. %C A161781 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.: %C A161781 (p,p+2,p+6) -> p+(0,2,6) => (0,1,3) -> 2^0 + 2^1 + 2^3 = 11. %C A161781 Each encoding is unique and so can be reversed e.g.: %C A161781 89 = 2^0 + 2^3 + 2^4 + 2^6 -> (0,3,4,6) => (p,p+6,p+8,p+12). %C A161781 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. %H A161781 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeConstellation.html">Prime Constellation</a>. %e A161781 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). %Y A161781 Cf. A008407, A020497, A094660, A135311. Also compare A014657 which is unrelated but remarkably similar. %K A161781 nonn %O A161781 0,2 %A A161781 _Carl R. White_, Jun 19 2009