A154391 Terms of A123466 which have a one-to-one correspondence between every run of 1's and 0's of the same length.

2, 10, 12, 38, 42, 44, 50, 52, 56, 142, 150, 154, 166, 170, 172, 178, 180, 184, 202, 204, 210, 212, 226, 232, 240, 542, 558, 570, 598, 602, 614, 618, 620, 654, 662, 666, 678, 682, 684, 690, 692, 696, 714, 716, 722, 724, 738, 744, 752, 796, 806, 810, 812, 818

Offset

1,1

Comments

Contribution from Leroy Quet, Aug 01 2009: (Start)

Each term of the sequence, when written in binary, has an even number of digits, since the same number of 0's occur in each binary representation as the number of 1's.

Each term of the sequence is even. (End)

Links

Lars Blomberg, Table of n, a(n) for n = 1..10000

Example

150 in binary is 10010110. There is a run of one 1, followed by a run of two 0's, followed by a run of one 1, followed by a run of one 0, followed by a run of two 1's, followed finally by a run of one 0. So the runs of 0's are of lengths (2,1,1), and the runs of 1's are of the lengths (1,1,2). Since (2,1,1) is a permutation of (1,1,2), then 150 is in the sequence. [From Leroy Quet, Aug 01 2009]

Mathematica

otocQ[n_]:=Module[{c=SortBy[Split[IntegerDigits[n, 2]], #[[1]]&]}, Length/@Select[c, #[[1]]==1&] == Length/@Select[c, #[[1]]==0&]]; Select[Range[1000], otocQ] (* Harvey P. Dale, Jul 13 2024 *)

Crossrefs

Cf. A123466.

Sequence in context: A055701 A176978 A186630 * A035928 A014486 A166751

Adjacent sequences: A154388 A154389 A154390 * A154392 A154393 A154394

Keyword

base,nonn

Author

Ray G. Opao, Jan 08 2009

Extensions

Extended, terms a(8)-a(11). Leroy Quet, Aug 01 2009

More terms from Lars Blomberg, Nov 07 2015

Status

approved