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A179529 Number of terms of A083207 in 12 consecutive numbers.

%I A179529 #7 Apr 30 2017 22:37:17
%S A179529 2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,3,3,4,4,3,3,3,3,2,2,2,2,2,2,2,2,2,2,
%T A179529 2,2,3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,2,2,3,3,2,2,2,2,2,2,2,2,
%U A179529 3,3,2,2,3,3,3,3,4,4,4,4,3,3,3,3,3,3,3,3,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,3
%N A179529 Number of terms of A083207 in 12 consecutive numbers.
%C A179529 a(n) = SUM(A179527(k): n <= k < n+12);
%C A179529 F. Buss and T. D. Noe conjectured a(n) > 0; this is correct (proof by R. Gerbicz);
%C A179529 a(n+1) = A179528(n+12) - A179528(n);
%C A179529 a(A179530(n)) = n and a(m) <> n for m < A179530(n).
%H A179529 R. Zumkeller, <a href="/A179529/b179529.txt">Table of n, a(n) for n = 1..10000</a>
%H A179529 Peter Luschny, <a href="http://www.luschny.de/math/seq/ZumkellerNumbers.html">Zumkeller Numbers</a>
%t A179529 ZumkellerQ[n_] := Module[{d = Divisors[n], t, ds, x}, ds = Total[d]; If[Mod[ds, 2] > 0, False, t = CoefficientList[Product[1 + x^i, {i, d}], x]; t[[1 + ds/2]] > 0]];
%t A179529 a[n_] := Sum[Boole[ZumkellerQ[k]], {k, n, n + 11}];
%t A179529 Array[a, 105] (* _Jean-François Alcover_, Apr 30 2017, after _T. D. Noe_ *)
%K A179529 nonn
%O A179529 1,1
%A A179529 _Reinhard Zumkeller_, Jul 19 2010