A261702 a(1) = 1; for n>1, a(n) is the smallest positive integer not already present which is entailed by the rules (i) k present => 2k present; (ii) 3k+1 present and k odd => k present.

1, 2, 4, 8, 16, 5, 10, 3, 6, 12, 20, 24, 32, 40, 13, 26, 48, 52, 17, 34, 11, 22, 7, 14, 28, 9, 18, 36, 44, 56, 64, 21, 42, 68, 72, 80, 84, 88, 29, 58, 19, 38, 76, 25, 50, 96, 100, 33, 66, 104, 112, 37, 74, 116, 128, 132, 136, 45, 90, 144, 148, 49, 98, 152

Offset

1,2

Comments

If the Collatz 3n+1 conjecture is true, then this is a permutation of all positive integers. See A261715 for putative inverse.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, PERL program for this sequence

Paul Tek, C++ program for this sequence

Index entries for sequences related to 3x+1 (or Collatz) problem

Maple

a:= proc() local a, b, s; b, s:= proc() true end,
      heap[new]((x, y)-> is(x>y), 1); a:=
      proc(n) option remember; local k, t;
        if n>1 then a(n-1) fi;
        t:= heap[extract](s); b(t):= false;
        k:= 2*t; if b(k) then heap[insert](k, s) fi;
        if irem(t-1, 3, 'k')=0 and (k::odd) and
          b(k) then heap[insert](k, s) fi; t
      end
    end():
seq(a(n), n=1..80);  # Alois P. Heinz, Aug 29 2015

Prog

(Perl) See Links section.
(C++) See Links section.

Crossrefs

Cf. A088975, A033491, A109732, A261690, A261715 (putative inverse).

Sequence in context: A110001 A302030 A167426 * A033491 A050076 A276070

Adjacent sequences: A261699 A261700 A261701 * A261703 A261704 A261705

Keyword

nonn,look

Author

Paul Tek, Aug 28 2015

Status

approved