cp's OEIS Frontend

A014306 a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.

%I A014306 #15 Oct 05 2018 11:17:15
%S A014306 0,0,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A014306 1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,
%U A014306 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0
%N A014306 a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.
%C A014306 a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). - _Reinhard Zumkeller_, Oct 14 2008
%C A014306 Characteristic function of A145397.
%H A014306 Antti Karttunen, <a href="/A014306/b014306.txt">Table of n, a(n) for n = 0..65537</a>
%H A014306 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%e A014306 From _David A. Corneth_, Oct 01 2018: (Start)
%e A014306 For n = 0, floor((6*0-1) ^ (1/3)) = -1. binomial(-1 + 2, 3) = n so a(0) = 0.
%e A014306 For n = 10, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) = n so a(10) = 0.
%e A014306 For n = 11, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) != n so a(11) = 1. (End)
%o A014306 (PARI) A014306(n) = { my(k=0); while(binomial(k+2,3)<n,k++); !(binomial(k+2,3)==n); }; \\ _Antti Karttunen_, Sep 30 2018
%o A014306 (PARI) a(n) = if(n==0, return(0)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) != n \\ _David A. Corneth_, Oct 01 2018
%o A014306 (PARI) first(n) = my(res = vector(n+1, i, 1), ov = nv = [1,2,1,0]); while(nv[4]<=n, res[nv[4]+1] = 0; for(i = 2, 4, nv[i] = ov[i-1] + ov[i]); ov = nv); res \\ _David A. Corneth_, Oct 01 2018
%Y A014306 Cf. A000292, A023533, A145397.
%K A014306 nonn,easy
%O A014306 0,1
%A A014306 _Clark Kimberling_
%E A014306 Data section extended up to a(120) by _Antti Karttunen_, Sep 30 2018