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A235202 Numbers written in an alternating binary-then-quaternary base.

%I A235202 #16 Jan 14 2014 00:25:51
%S A235202 1,10,11,20,21,30,31,100,101,110,111,120,121,130,131,1000,1001,1010,
%T A235202 1011,1020,1021,1030,1031,1100,1101,1110,1111,1120,1121,1130,1131,
%U A235202 2000,2001,2010,2011,2020,2021,2030,2031,2100
%N A235202 Numbers written in an alternating binary-then-quaternary base.
%C A235202 Mixed-radix number representation produced by a serial counter with generating sequence (1, 3, 1, 3, ...) = A010684.
%C A235202 Places reading from the right have values (1, 2, 8, 16, 64, 128, ...) = unsigned A094014.
%C A235202 Conjecture: This sequence interpreted as quaternary (base 4) numbers gives A126001 (hence a simplified scheme for computing that sequence).
%H A235202 Jeremy Gardiner, <a href="/A235202/b235202.txt">Table of n, a(n) for n = 1..1024</a>
%e A235202 a(15) = 131 since 15 = 1*1+3*2+1*8.
%o A235202 (Chipmunk BASIC) # see www.nicholson.com/rhn/basic/
%o A235202 do : rem serial counter
%o A235202 z=z+1
%o A235202 if z>1 then z=0 : y=y+1
%o A235202 if y>3 then y=0 : x=x+1
%o A235202 if x>1 then x=0 : w=w+1
%o A235202 if w>3 then print : end
%o A235202 s$=str$(w)+str$(x)+str$(y)+str$(z)
%o A235202 c=val(s$) : rem strip leading zeros
%o A235202 print str$(c)+", ";
%o A235202 loop
%Y A235202 Cf. A109827 (Numbers written in an alternating binary-then-ternary base).
%K A235202 nonn,base
%O A235202 1,2
%A A235202 _Jeremy Gardiner_, Jan 04 2014