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

1,3

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.

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.

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).

Example

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

Mathematica

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

Crossrefs

Cf. A000975, A007088, A007090.

Sequence in context: A132600 A163627 A189887 * A018431 A184350 A347657

Adjacent sequences: A179967 A179968 A179969 * A179971 A179972 A179973

Keyword

base,nonn,easy

Author

Reinhard Zumkeller, Aug 04 2010

Status

approved