login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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: A002734 A160100 A247891 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 15 03:28 EDT 2019. Contains 328025 sequences. (Running on oeis4.)