## S000681

An encoding of prime constellations.

1, 5, 17, 65, 69, 81, 257, 261, 321, 325, 1025, 1041, 1089, 1105, 4097, 4101, 4113, 4161, 4165, 4177, 4353, 4357, 4417, 4421, 5121, 5137, 5185, 5201, 16385, 16389, 16449, 16453, 16641, 16645, 16705, 20481, 20485, 20545, 20549, 20737, 20741, 65537, 65553

1

To generate the first 160 terms of this sequence, nn was set to 21 in the Mathematica program below. The runtime for nn=21 is measured in days. This sequence is similar to A161781, which removes the zeros from the binary numbers.

T. D. Noe, Plot of 160 terms

T. D. Noe, Table of 160 terms

Example: 81 = 64+16+1 is the encoding of prime triples of the form {k, k+2, k+6}.

(Mma) nn = 12; t2 = {}; Do[t = {}; f = Flatten[Position[IntegerDigits[q, 2], 1] - 1]; If[And @@ EvenQ[f], n = 1; While[ps = f + n; If[And @@ PrimeQ[ps], AppendTo[t, n]]; Length[t] < 100 && n < 100000001, n = n + 2]; If[Length[t] > 1, AppendTo[t2, q]; Print[{q, t[[1]], t[[-1]], Length[t], f}]]], {q, 1, 2^nn - 1, 2}]; t2

Cf. A161781, S000682, S000683.

nonn,hard,nice

T. D. Noe, Jul 09 2015

© Tony D Noe 2014-2015