%I A007090 M0900
%S A007090 0,1,2,3,10,11,12,13,20,21,22,23,30,31,32,33,100,101,102,103,110,111,112,
%T A007090 113,120,121,122,123,130,131,132,133,200,201,202,203,210,211,212,213,
%U A007090 220,221,222,223,230,231,232,233,300,301,302,303,310,311,312,313,320
%N A007090 Numbers in base 4.
%C A007090 Contribution from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 25 
               2009: (Start)
%C A007090 Nonnegative integers with no decimal digit > 3.
%C A007090 Thus nonnegative integers in base 10 whose tripling (trebling) by normal 
               addition or multiplication requires no carry operation. (End)
%D A007090 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A007090 a(n)=Sum{d(i)*10^i: i=0, 1, ..., m}, where Sum{d(i)*4^i: i=0, 1, ..., 
               m} is the base 4 representation of n.
%F A007090 a(0)=0 a(n)=10*a(n/4) if n==0 (mod 4) a(n)=a(n-1)+1 otherwise. - Benoit 
               Cloitre, Dec 22, 2002
%t A007090 Table[ FromDigits[ IntegerDigits[n, 4]], {n, 0, 60}]
%o A007090 (PARI) a(n)=if(n<1,0,if(n%4,a(n-1)+1,10*a(n/4)))
%Y A007090 Cf. A007608, A000042, A007088, A007089, A007091, A007092, A007093, A007094 
               & A007095.
%Y A007090 Sequence in context: A141670 A074068 A055655 this_sequence A102859 A123977 
               A069967
%Y A007090 Adjacent sequences: A007087 A007088 A007089 this_sequence A007091 A007092 
               A007093
%K A007090 nonn,base
%O A007090 0,3
%A A007090 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)