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

1,2

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).

Links

Table of n, a(n) for n=1..47.

Example

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.

Prog

(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) }
{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)}

Crossrefs

Sequence in context: A053069 A178504 A193733 * A130842 A061818 A166938

Adjacent sequences: A167500 A167501 A167502 * A167504 A167505 A167506

Keyword

nonn,base

Author

M. F. Hasler, Nov 05 2009

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

Status

approved