A165404 The positions of zeros in the top row of A163898 (and A163899).

0, 1, 4, 6, 7, 16, 18, 19, 24, 25, 28, 30, 31, 64, 66, 67, 72, 73, 76, 78, 79, 96, 97, 100, 102, 103, 112, 114, 115, 120, 121, 124, 126, 127, 256, 258, 259, 264, 265, 268, 270, 271, 288, 289, 292, 294, 295, 304, 306, 307, 312, 313, 316, 318, 319, 384, 385, 388

Offset

0,3

Comments

Equivalently, the positions of ones in the top row of A163904.

From Jeffrey Shallit, Jan 18 2026: (Start)

k is in the sequence if and only if the automaton given in the Shallit link accepts the binary representation of k.

Equivalently, k is in the sequence if and only if A163482(k) = A000695(k). (End)

k is in the sequence if and only if it is the encoding of the possible contents of pin 2 when carrying out the optimal algorithm for the Hanoi tower problem on infinitely many disks. For example, the fact that 6 is in the sequence, but not 5, indicates that pin 2 holds disks 1 and 2 at some point, but never disks 0 and 2. - Jeffrey Shallit, Feb 09 2026

Links

Antti Karttunen, Table of n, a(n) for n = 0..609

Jeffrey Shallit, Automaton accepting members of A165404.

Formula

a(n) = A025581(A165403(n)).

Crossrefs

Cf. A025581, A165403, A392655.

Same sequence in binary: A165406. For n>0, A147600(n-1) seems to give the number of terms with binary width n. See also A163901.

Sequence in context: A379961 A102141 A107919 * A270887 A213034 A102131

Adjacent sequences: A165401 A165402 A165403 * A165405 A165406 A165407

Keyword

nonn

Author

Antti Karttunen, Sep 19 2009

Status

approved