A113820 - OEIS

A113820

Triangle where 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 do not have any 1-bits in the same position when they are written in binary.

2, 1, 4, 8, 12, 16, 3, 9, 10, 11, 18, 24, 26, 32, 34, 17, 25, 33, 40, 41, 48, 56, 64, 72, 80, 88, 96, 104, 5, 6, 7, 19, 20, 21, 22, 23, 36, 38, 50, 52, 54, 66, 68, 70, 82, 37, 49, 53, 65, 69, 81, 84, 85, 97, 100, 112, 116, 128, 132, 144, 148, 160, 164, 176, 180, 192, 35, 51

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Sequence is a permutation of the positive integers.

Among first 2001000 terms (2000 rows) this permutation has fixed points 38, 195, 62107 and 1286571, 2-cycle (1,2) and 3-cycles (11603,13126,13397) and (176377,187821,298266).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Rémy Sigrist, PARI program

EXAMPLE

4 = 100 in binary. Among the positive integers not occurring among the first 3 rows of the sequence (3 = 11 in binary, 5 = 101 in binary, 7 = 111 in binary, etc...), [3,9,10,11] (which is [11,1001,1010,1011] in binary) are the lowest 4 positive integers that do not share any 1-bits with 4 when written in binary. So row 4 is [3,9,10,11].

PROG

(PARI) See Links section.

CROSSREFS

Cf. A115629 (inverse).

Row sums are in A160968. [From Klaus Brockhaus, May 31 2009]

Sequence in context: A363386 A294104 A294061 * A319479 A303632 A133267

Adjacent sequences: A113817 A113818 A113819 * A113821 A113822 A113823

KEYWORD

easy,nonn,tabl,base

AUTHOR

Leroy Quet, Jan 23 2006

EXTENSIONS

Corrected and extended by Klaus Brockhaus, Jan 27 2006

STATUS

approved