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

1,1

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

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 *)

Crossrefs

Cf. A062880, A007090.

Sequence in context: A043051 A024545 A101134 * A055046 A141386 A254220

Adjacent sequences: A045107 A045108 A045109 * A045111 A045112 A045113

Keyword

nonn,base

Author

Clark Kimberling

Status

approved