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User: Christophe Papazian

Christophe Papazian has authored 1 sequences.

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

Christophe Papazian, Jul 24 2019

nonn

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

			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}).

Wikipedia, Hereditarily finite set
Wikipedia, Transitive set

Cf. A034797, A102553.

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 *)

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

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User: Christophe Papazian

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

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