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

1,3

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

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);

Crossrefs

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

Sequence in context: A039273 A039164 A263977 * A270427 A270189 A257672

Adjacent sequences: A335037 A335038 A335039 * A335041 A335042 A335043

Keyword

nonn,base

Author

Alois P. Heinz, May 20 2020

Status

approved