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.

%I #13 Jun 10 2022 06:13:32

%S 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,

%T 88,96,104,5,6,7,19,20,21,22,23,36,38,50,52,54,66,68,70,82,37,49,53,

%U 65,69,81,84,85,97,100,112,116,128,132,144,148,160,164,176,180,192,35,51

%N 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.

%C Sequence is a permutation of the positive integers.

%C 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).

%H Rémy Sigrist, <a href="/A113820/b113820.txt">Table of n, a(n) for n = 1..10011</a>

%H Rémy Sigrist, <a href="/A113820/a113820.gp.txt">PARI program</a>

%e 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].

%o (PARI) See Links section.

%Y Cf. A115629 (inverse).

%Y Row sums are in A160968. [From _Klaus Brockhaus_, May 31 2009]

%K easy,nonn,tabl,base

%O 1,1

%A _Leroy Quet_, Jan 23 2006

%E Corrected and extended by _Klaus Brockhaus_, Jan 27 2006