A328732 - OEIS

%I #17 Dec 18 2024 09:27:20

%S 0,-1,1,-2,2,-3,-1,1,3,-4,4,-5,-3,3,5,-6,-2,2,6,-7,-5,-3,-1,1,3,5,7,

%T -8,8,-9,-7,7,9,-10,-6,6,10,-11,-9,-7,-5,5,7,9,11,-12,-4,4,12,-13,-11,

%U -5,-3,3,5,11,13,-14,-10,-6,-2,2,6,10,14

%N Irregular table read by rows; for any n >= 0, the n-th row contains the numbers of the form u - v with u + v = n and u AND v = 0 (where AND denotes the bitwise AND operator), in ascending order.

%C The n-th row:

%C - has A001316(n) terms,

%C - has -n as first term and n as last term,

%C - has least positive term T(n, A001316(n)/2+1) = A080079(n) (when n > 0).

%H Rémy Sigrist, <a href="/A328732/b328732.txt">Table of n, a(n) for n = 0..6562</a> (Rows for n = 0..256)

%H Rémy Sigrist, <a href="/A328732/a328732.png">Scatterplot of (n, T(n, k)) for n = 0..1024 and k = 1..A001316(n)</a>

%e Table begins:

%e     0;

%e    -1,   1;

%e    -2,   2;

%e    -3,  -1,   1,   3;

%e    -4,   4;

%e    -5,  -3,   3,   5;

%e    -6,  -2,   2,   6;

%e    -7,  -5,  -3,  -1,   1,   3,   5,   7;

%e    -8,   8;

%e    -9,  -7,   7,   9;

%e   -10,  -6,   6,  10;

%e   -11,  -9,  -7,  -5,   5,   7,   9,  11;

%e   -12,  -4,   4,  12;

%e   -13, -11,  -5,  -3,   3,   5,  11,  13;

%e   ...

%o (PARI) row(n) = my (r=[0], b=Vecrev(binary(n))); for (k=0, #b-1, if (b[k+1], r=concat(apply(v -> [v-2^k,v+2^k], r)))); Set(r)

%Y Cf. A001316, A080079.

%K sign,base,tabf

%O 0,4

%A _Rémy Sigrist_, Oct 26 2019