A045110 Numbers whose base-4 representation contains no 1's and exactly one 3.

3, 11, 12, 14, 35, 43, 44, 46, 48, 50, 56, 58, 131, 139, 140, 142, 163, 171, 172, 174, 176, 178, 184, 186, 192, 194, 200, 202, 224, 226, 232, 234, 515, 523, 524, 526, 547, 555, 556, 558, 560, 562, 568, 570, 643, 651, 652, 654, 675

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

From Robert Israel, Apr 10 2018: (Start)

If k is in the sequence, then so are 4*k and 4*k+2.

All even terms of the sequence are obtained in this way.

The odd terms of the sequence are 4*k+3 for k in A062880. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062880, A007090.

Programs

Maple

f:= proc(i,x,d) local j,X, nX;
     X:= convert(x,base,2); nX:= nops(X);
     3*4^i+add(X[j]*2*4^`if`(j<=i,j-1,j),j=1..nX)
end proc:
sort([seq(seq(seq(f(i,x,d),x=`if`(i=d-1,0,2^(d-2))..2^(d-1)-1),i=0..d-1),d=0..6)]); # Robert Israel, Apr 10 2018

Mathematica

Select[Range[700],DigitCount[#,4,1]==0&&DigitCount[#,4,3]==1&] (* Harvey P. Dale, Jul 23 2018 *)