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

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, 78, 100, 102, 108, 110, 145, 147, 153, 155, 177, 179, 185, 187, 196, 198, 204, 206, 228, 230, 236, 238, 273, 275, 281, 283, 305, 307, 313, 315, 401, 403, 409, 411, 433, 435

Offset: 1

Author

Reinhard Zumkeller, Aug 04 2010

Keywords

• base
• nonn
• easy

Comments

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

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

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

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

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

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

Examples

			a(10)=14->base4:32->base2:1110;
a(100)=1126->base4:101212->base2:10001100110;
a(1000)=113043->base4:123212103->base2:11011100110010011.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Quaternary
• Index entries for 2-automatic sequences.

Crossrefs

Cf. A000975, A007088, A007090.

Programs

Mathematica

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

Formula

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

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