A335042 Numbers whose binary representation encodes a (binary) max-heap on elements from the set {0,1} with root at the most significant bit and a min-heap with root at the least significant bit.

0, 1, 2, 3, 4, 6, 7, 8, 10, 12, 14, 15, 16, 20, 24, 26, 28, 30, 31, 32, 40, 48, 52, 56, 58, 60, 62, 63, 64, 80, 96, 100, 104, 108, 112, 116, 120, 122, 124, 126, 127, 128, 160, 192, 200, 208, 216, 224, 228, 232, 236, 240, 244, 248, 250, 252, 254, 255, 256, 320

Offset: 1

Author

Alois P. Heinz, May 20 2020

Keywords

• nonn
• base

Comments

All odd terms are in A000225.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Heap
• Wikipedia, Binary heap
• Wikipedia, Least significant bit
• Wikipedia, Most significant bit

Crossrefs

Cf. A000225 (subsequence), A335039, A335040, A335041.

Programs

Maple

q:= proc(n) local i, l; l:= convert(n, base, 2);
      for i from 2 to nops(l) do if (h-> l[i]l[-h])(iquo(i, 2)) then return false fi
      od; true
    end:
a:= proc(n) option remember; local k: for k from 1+
      `if`(n=1, -1, a(n-1)) while not q(k) do od; k
    end:
seq(a(n), n=1..62);

Formula

{ A335040 } intersect { A335041 }.