A071674 - OEIS

%I #11 Aug 22 2021 22:38:13

%S 0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0,

%T 0,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0,1,1,0,0,0,1,0,0,1,0,1,1,1,0,1,0,0,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,0,0,1,0,0

%N Sequence A071673 reduced modulo 2.

%H Antti Karttunen, <a href="/A071674/b071674.txt">Table of n, a(n) for n = 0..10440 (rows 0..144 of the triangle, flattened)</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A000035(A071673(n)).

%e The first 15 rows of this irregular triangular table:

%e   0,

%e   1,

%e   0, 0,

%e   1, 1, 1,

%e   1, 0, 0, 1,

%e   0, 0, 1, 0, 0,

%e   0, 1, 1, 1, 1, 0,

%e   0, 1, 0, 1, 0, 1, 0,

%e   0, 1, 0, 0, 0, 0, 1, 0,

%e   1, 1, 0, 0, 1, 0, 0, 1, 1,

%e   1, 0, 0, 0, 1, 1, 0, 0, 0, 1,

%e   0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0,

%e   1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e   1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1,

%e   0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0,

%e etc.

%o (PARI)

%o up_to = 10440;

%o A002260(n) = (n-binomial((sqrtint(8*n)+1)\2, 2)); \\ From A002260

%o A004736(n) = (1-n+(n=sqrtint(8*n)\/2)*(n+1)\2); \\ From A004736

%o A071673list(up_to) = { my(v=vector(1+up_to)); v[1] = 0; for(n=1,up_to,v[1+n] = 1 + v[A004736(n)] + v[A002260(n)]); (v); };

%o v071673 = A071673list(up_to);

%o A071673(n) = v071673[1+n];

%o A071674(n) = (A071673(n)%2); \\ _Antti Karttunen_, Aug 22 2021

%Y Cf. A000035, A071673.

%K nonn,tabf

%O 0

%A _Antti Karttunen_, May 30 2002

%E Term a(0) = 0 prepended and the Example section added by _Antti Karttunen_, Aug 22 2021