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A331829 Positive numbers k such that k and k + 1 are both positive negabinary-Niven numbers (A331728) and -k and -(k + 1) are both negative negabinary-Niven numbers (A331819).

%I A331829 #8 Jan 29 2020 01:42:17
%S A331829 2,3,8,15,32,63,128,174,245,255,512,1023,1085,1295,1505,1854,1925,
%T A331829 2048,2744,3248,3303,3752,4025,4095,4760,4815,4865,5004,5319,5768,
%U A331829 6327,6776,7104,7784,7944,8154,8192,8574,8792,8855,9800,10254,10808,11312,11816,11871
%N A331829 Positive numbers k such that k and k + 1 are both positive negabinary-Niven numbers (A331728) and -k and -(k + 1) are both negative negabinary-Niven numbers (A331819).
%C A331829 Positive numbers k such that both k and k + 1 are in A331827.
%C A331829 Numbers of the form 2^(2*k+1) and 2^(2*k) - 1 are terms.
%H A331829 Amiram Eldar, <a href="/A331829/b331829.txt">Table of n, a(n) for n = 1..10000</a>
%t A331829 negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; negBinQ[n_] := And @@ (Divisible[n, negaBinWt[#]] & /@ {-n, n}); nConsec = 2; neg = negBinQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negBinQ[k]}]; k++]; seq
%Y A331829 Intersection of A331820 and A331821.
%Y A331829 Cf. A331092, A331728, A331819, A331827.
%K A331829 nonn,base
%O A331829 1,1
%A A331829 _Amiram Eldar_, Jan 28 2020