A335039 Numbers whose binary representation encodes a (binary) max-heap on elements from the set {0,1} with root at the least significant bit.

0, 1, 3, 5, 7, 11, 15, 19, 23, 27, 31, 37, 39, 47, 55, 63, 69, 71, 79, 87, 95, 101, 103, 111, 119, 127, 139, 143, 155, 159, 175, 191, 207, 223, 239, 255, 267, 271, 283, 287, 303, 319, 335, 351, 367, 383, 395, 399, 411, 415, 431, 447, 463, 479, 495, 511, 531

Offset: 1

Author

Alois P. Heinz, May 20 2020

Keywords

• nonn
• base

Comments

All positive terms are odd.

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

Crossrefs

Cf. A000225 (subsequence), A335040, A335041, A335042.

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..59);