A309274 Ackermann Coding (BIT predicate) of transitive hereditarily finite sets.

0, 1, 3, 7, 11, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 119, 127, 135, 143, 151, 159, 167, 175, 183, 191, 199, 207, 215, 223, 231, 239, 247, 255, 267, 271, 287, 303, 319, 335, 351, 367, 383, 399, 415, 431, 447, 463, 479, 495, 511, 523, 527, 543

Offset

1,3

Comments

If the representation of a(n) in base 2 contains the k-th bit (2^k), then it must contain the bits of k.

A034797 is a subsequence, and can be seen as a recursive variant of this sequence. - Rémy Sigrist, Jul 25 2019

Links

Table of n, a(n) for n=1..56.

Wikipedia, Hereditarily finite set

Wikipedia, Transitive set

Example

23 is in the sequence because 23 = 2^4 + 2^2 + 2^1 + 2^0 encodes the transitive set {0,1,{1},{{1}}} (remember that 0 is the empty set and 1 is {0}).

Mathematica

b[n_] := (Flatten @ Position[Reverse[IntegerDigits[n, 2]], 1] - 1);
okQ[n_] := With[{bb = b[n]}, AllTrue[b /@ bb, Intersection[bb, #] == #&]];
Select[Range[0, 600], okQ] (* Jean-François Alcover, Jul 25 2019 *)

Prog

(PARI) is(n) = { for (b=0, #binary(n), if (bittest(n, b), if (bitand(n, b)!=b, return (0)))); return (1) } \\ Rémy Sigrist, Jul 25 2019

Crossrefs

Cf. A034797, A102553.

Sequence in context: A243115 A279106 A172306 * A112714 A327330 A231348

Adjacent sequences: A309271 A309272 A309273 * A309275 A309276 A309277

Keyword

nonn

Author

Christophe Papazian, Jul 24 2019

Status

approved