A179970 - OEIS

%I #14 Feb 13 2017 01:14:56

%S 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 78,100,102,108,110,145,147,153,155,177,179,185,187,196,198,204,206,

%U 228,230,236,238,273,275,281,283,305,307,313,315,401,403,409,411,433,435

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

%C If m is a term with m mod 4 < 2 then is also m+2 a term;

%C 0 <= a(2*n-1) mod 4 <= 1 and 2 <= a(2*n) mod 4 <= 3;

%C a(n) mod 2 = 1 - a(floor((n-1)/2)) mod 2;

%C a(n) mod 4 = a(n) mod 2 + 2*(1 - n mod 2);

%C floor(a(n)/4) = a(floor((n-1)/2));

%C in binary representation there are no runs of more than 3 zeros or 3 ones: subsequence of A166535.

%H R. Zumkeller, <a href="/A179970/b179970.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Quaternary.html">Quaternary</a>

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%F Let m = a(floor((n-1)/2)), then for n > 3:

%F a(n) = 4*m - m mod 2 + 1 + 2*(1 - n mod 2).

%e a(10)=14->base4:32->base2:1110;

%e a(100)=1126->base4:101212->base2:10001100110;

%e a(1000)=113043->base4:123212103->base2:11011100110010011.

%t Select[Range[0,500],And@@OddQ[Total/@Partition[IntegerDigits[#,4],2,1]]&] (* _Harvey P. Dale_, Aug 19 2012 *)

%Y Cf. A000975, A007088, A007090.

%K base,nonn,easy

%O 1,3

%A _Reinhard Zumkeller_, Aug 04 2010