A167503 Positions of nonzero digits in this sequence, where the terms are written in base 3 (and concatenated).

1, 2, 10, 12, 20, 21, 100, 101, 102, 112, 121, 122, 201, 202, 210, 211, 212, 220, 221, 222, 1000, 1001, 1002, 1011, 1012, 1021, 1022, 1100, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1200, 1202, 1210, 1211, 1212, 1220, 1221, 1222, 2010, 2020, 2021, 2101

Offset: 1

Author

M. F. Hasler, Nov 05 2009

Keywords

• nonn
• base

Comments

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).

Examples

			The list cannot start with 0 (cf. A167500), so the first digit of the sequence is nonzero, whence a(1)=1.
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.
For the same reason, a(3) = 3[10] = 10[3]. (All terms are written in base 3.)
Thus the 4th digit is zero, followed by the m.s.d. of the next term which is nonzero, thus a(4)=5.
Terms of the sequence:_ 1,2,10,12,20,21,100,101
Position of the digits: 1 2 34 56 78 9A BCD EFG (A=10,...)
Thus the numbers 4,8,12,13,15,..., which give the positions of digits '0', are not in this sequence.
		

Programs

PARI

base(n,b=3,s=1) = { my( a=[ n%b ]); while( 0=n & for(i=a[n-1]+1,#b,b[i] & (a=concat(a,i)) & break); #a
				

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010