A335040 Numbers whose binary representation encodes a (binary) max-heap on elements from the set {0,1} with root at the most significant bit.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 20, 24, 25, 26, 27, 28, 29, 30, 31, 32, 40, 41, 48, 50, 52, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 80, 81, 82, 83, 96, 100, 104, 108, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126

Offset: 1

Author

Alois P. Heinz, May 20 2020

Keywords

• nonn
• base

Links

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

Crossrefs

Cf. A000225 (subsequence), A335039, A335041, A335042 (subsequence).

Programs

Maple

q:= proc(n) local i, l; l:= convert(n, base, 2);
      for i from 2 to nops(l) do
        if l[-i]>l[-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..70);