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

1,3

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

Formula

{ A335040 } intersect { A335041 }.

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]
        or 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);

Crossrefs

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

Sequence in context: A334274 A225620 A335041 * A257282 A336488 A221178

Adjacent sequences: A335039 A335040 A335041 * A335043 A335044 A335045

Keyword

nonn,base

Author

Alois P. Heinz, May 20 2020

Status

approved