A167503 - OEIS

%I #5 Jul 14 2012 11:32:32

%S 1,2,10,12,20,21,100,101,102,112,121,122,201,202,210,211,212,220,221,

%T 222,1000,1001,1002,1011,1012,1021,1022,1100,1102,1110,1111,1112,1120,

%U 1121,1122,1200,1202,1210,1211,1212,1220,1221,1222,2010,2020,2021,2101

%N Positions of nonzero digits in this sequence, where the terms are written in base 3 (and concatenated).

%C This sequence lists the positions of nonzero digits in the sequence, where the terms are written in base 3 and concatenated, such that the least significant digit (units) of a(n) is followed by the most significant digit of a(n+1).

%e The list cannot start with 0 (cf. A167500), so the first digit of the sequence is nonzero, whence a(1)=1.

%e The next nonzero digit of this sequence will be the most significant digit (m.s.d.) of a(2), necessarily nonzero, thus a(2)=2.

%e For the same reason, a(3) = 3[10] = 10[3]. (All terms are written in base 3.)

%e Thus the 4th digit is zero, followed by the m.s.d. of the next term which is nonzero, thus a(4)=5.

%e Terms of the sequence:_ 1,2,10,12,20,21,100,101

%e Position of the digits: 1 2 34 56 78 9A BCD EFG (A=10,...)

%e Thus the numbers 4,8,12,13,15,..., which give the positions of digits '0', are not in this sequence.

%o (PARI) base(n,b=3,s=1) = { my( a=[ n%b ]); while( 0<n\=b, a=concat( n%b, a )); if( s, eval( Strchr( vectorsmall( #a,i,48+a[i] ))), a) }

%o {a=b=[]; for(n=1,99, #b>=n & for(i=a[n-1]+1,#b,b[i] & (a=concat(a,i)) & break); #a<n & a=concat(a,#b+1); b=concat(b,base(a[n],3,0))); apply(base,a)}

%K nonn,base

%O 1,2

%A _M. F. Hasler_, Nov 05 2009

%E Edited by _Charles R Greathouse IV_, Aug 02 2010