cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A099026 Array x AND NOT y, read by rising antidiagonals.

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%I A099026 #22 Sep 30 2024 12:52:46
%S A099026 0,1,0,2,0,0,3,2,1,0,4,2,0,0,0,5,4,1,0,1,0,6,4,4,0,2,0,0,7,6,5,4,3,2,
%T A099026 1,0,8,6,4,4,0,2,0,0,0,9,8,5,4,1,0,1,0,1,0,10,8,8,4,2,0,0,0,2,0,0,11,
%U A099026 10,9,8,3,2,1,0,3,2,1,0,12,10,8,8,8,2,0,0,4,2,0,0,0,13,12,9,8,9,8,1
%N A099026 Array x AND NOT y, read by rising antidiagonals.
%C A099026 For n>0, the n-th row and the differences of the n-th column have period 2^floor(log_(n)+1).
%H A099026 Rémy Sigrist, <a href="/A099026/b099026.txt">Table of n, a(n) for n = 0..10010</a>
%H A099026 Rémy Sigrist, <a href="/A099026/a099026.png">Colored representation of the table for n, k < 2^10</a> (the color at (x, y) is function of T(x, y))
%F A099026 T(x, y) = x AND NOT y. The AND NOT operation satisfies the bitwise truth table: (0, 0) = 0, (0, 1) = 0, (1, 0) = 1, (1, 1) = 0.
%e A099026 0,0,0,0,0,0,
%e A099026 1,0,1,0,1,0,
%e A099026 2,2,0,0,2,2,
%e A099026 3,2,1,0,3,2,
%e A099026 4,4,4,4,0,0,
%e A099026 5,4,5,4,1,0,
%t A099026 Table[BitAnd[x - y, BitNot[y]], {x, 0, 15}, {y, 0, x}] (* _Paolo Xausa_, Sep 30 2024 *)
%o A099026 (PARI) T(x,y)=bitnegimply(x,y)
%Y A099026 Rows include A000004, A059841. Columns include A001477, A052928. Antidiagonal sums are in A099027.
%Y A099026 Cf. A003985 (AND), A003986 (OR), A003987 (XOR).
%K A099026 nonn,tabl,base
%O A099026 0,4
%A A099026 _Ralf Stephan_, Sep 26 2004