A113821 Triangle where a(1,1)=1; and the n terms of row n are the smallest positive integers not occurring earlier in the sequence such that, for any given m (1 <= m <= n), a(n,m) and n have at least one 1-bit in the same position when they are written in binary.

1, 2, 3, 5, 6, 7, 4, 12, 13, 14, 9, 11, 15, 17, 19, 10, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 8, 24, 40, 41, 42, 43, 44, 45, 33, 35, 37, 39, 46, 47, 49, 51, 53, 34, 38, 50, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 69, 70, 71, 72, 73, 36, 52, 68, 74, 75, 76, 77

Offset

1,2

Comments

Sequence is a permutation of the positive integers.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (Rows 1 <= n <= 150).

Example

4 = 100 in binary. Among the positive integers not occurring among the first 3 rows of the sequence (4 = 100 in binary, 8 = 1000 in binary, 9 = 1001 in binary, etc...), [4,12,13,14] (which is [100,1100,1101,1110] in binary) are the lowest 4 positive integers that share at least one 1-bit with 4 when written in binary. So row 4 is [4,12,13,14].
From Michael De Vlieger, Aug 16 2017: (Start)
Triangle begins:
   1
   2   3
   5   6   7
   4  12  13  14
   9  11  15  17  19
  10  18  20  21  22  23
  25  26  27  28  29  30  31
   8  24  40  41  42  43  44  45
  33  35  37  39  46  47  49  51  53
  34  38  50  54  55  56  57  58  59  60
  61  62  63  65  66  67  69  70  71  72  73
  36  52  68  74  75  76  77  78  79  84  85  86
  ...
(End)

Mathematica

Block[{a = {{1}}}, Do[a = Join[a, {Take[#, n]}] &@ Select[Flatten@ Position[Array[BitAnd[n, #] &, 120], k_ /; k > 0], FreeQ[a, #] &], {n, 2, 12}]; Flatten@ a] (* Michael De Vlieger, Aug 16 2017 *)

Crossrefs

Cf. A115630 (inverse), A115640 (fixed points), A115641 (cycles), A115642 (cycle lengths).

Row sums are in A160969. - Klaus Brockhaus, May 31 2009

Sequence in context: A247891 A367407 A354370 * A319523 A255367 A280098

Adjacent sequences: A113818 A113819 A113820 * A113822 A113823 A113824

Keyword

easy,nonn,tabl

Author

Leroy Quet, Jan 23 2006

Extensions

More terms from Klaus Brockhaus, Jan 29 2006

Status

approved