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A179970 Numbers such that in base-4 representation all sums of two adjacent digits are odd.

%I A179970 #15 Feb 16 2025 08:33:12
%S A179970 0,1,2,3,4,6,9,11,12,14,17,19,25,27,36,38,44,46,49,51,57,59,68,70,76,
%T A179970 78,100,102,108,110,145,147,153,155,177,179,185,187,196,198,204,206,
%U A179970 228,230,236,238,273,275,281,283,305,307,313,315,401,403,409,411,433,435
%N A179970 Numbers such that in base-4 representation all sums of two adjacent digits are odd.
%C A179970 If m is a term with m mod 4 < 2 then is also m+2 a term;
%C A179970 0 <= a(2*n-1) mod 4 <= 1 and 2 <= a(2*n) mod 4 <= 3;
%C A179970 a(n) mod 2 = 1 - a(floor((n-1)/2)) mod 2;
%C A179970 a(n) mod 4 = a(n) mod 2 + 2*(1 - n mod 2);
%C A179970 floor(a(n)/4) = a(floor((n-1)/2));
%C A179970 in binary representation there are no runs of more than 3 zeros or 3 ones: subsequence of A166535.
%H A179970 R. Zumkeller, <a href="/A179970/b179970.txt">Table of n, a(n) for n = 1..10000</a>
%H A179970 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Quaternary.html">Quaternary</a>
%H A179970 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A179970 Let m = a(floor((n-1)/2)), then for n > 3:
%F A179970 a(n) = 4*m - m mod 2 + 1 + 2*(1 - n mod 2).
%e A179970 a(10)=14->base4:32->base2:1110;
%e A179970 a(100)=1126->base4:101212->base2:10001100110;
%e A179970 a(1000)=113043->base4:123212103->base2:11011100110010011.
%t A179970 Select[Range[0,500],And@@OddQ[Total/@Partition[IntegerDigits[#,4],2,1]]&] (* _Harvey P. Dale_, Aug 19 2012 *)
%Y A179970 Cf. A000975, A007088, A007090.
%K A179970 base,nonn,easy
%O A179970 1,3
%A A179970 _Reinhard Zumkeller_, Aug 04 2010