cp's OEIS Frontend

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

%I A045110 #18 May 21 2023 12:28:19
%S A045110 3,11,12,14,35,43,44,46,48,50,56,58,131,139,140,142,163,171,172,174,
%T A045110 176,178,184,186,192,194,200,202,224,226,232,234,515,523,524,526,547,
%U A045110 555,556,558,560,562,568,570,643,651,652,654,675
%N A045110 Numbers whose base-4 representation contains no 1's and exactly one 3.
%C A045110 From _Robert Israel_, Apr 10 2018: (Start)
%C A045110 If k is in the sequence, then so are 4*k and 4*k+2.
%C A045110 All even terms of the sequence are obtained in this way.
%C A045110 The odd terms of the sequence are 4*k+3 for k in A062880. (End)
%H A045110 Robert Israel, <a href="/A045110/b045110.txt">Table of n, a(n) for n = 1..10000</a>
%p A045110 f:= proc(i,x,d) local j,X, nX;
%p A045110      X:= convert(x,base,2); nX:= nops(X);
%p A045110      3*4^i+add(X[j]*2*4^`if`(j<=i,j-1,j),j=1..nX)
%p A045110 end proc:
%p A045110 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
%t A045110 Select[Range[700],DigitCount[#,4,1]==0&&DigitCount[#,4,3]==1&] (* _Harvey P. Dale_, Jul 23 2018 *)
%Y A045110 Cf. A062880, A007090.
%K A045110 nonn,base
%O A045110 1,1
%A A045110 _Clark Kimberling_