A097580 Base 3 representation of the concatenation of the first n numbers with the most significant digits first.

1, 110, 11120, 1200201, 121221020, 20021100110, 2022201111201, 212020020002100, 22121022020212200, 1011212101120110200001, 11101000122011021220211010, 121012010100112220022220220120

Offset: 1

Author

Cino Hilliard, Aug 29 2004

Keywords

• base
• nonn

Comments

Consider numbers of the form 1, 12, 123, 1234, ..., N. Find the highest power of 3^p such that 3^p <= N. Then p = [log(N)/log(3)] and for 0 <= qi <= 2 [N/3^p] = q1 + r1 [r1/3^(p-1)] = q2 + r2 ........................ rp/3^1 = qp + rp+1 rp+1/3^0 = qp+1 0 For N = 1234, p = [log(1234)/log(3)] = 6 division quot rem 1234/3^6 = 1 505 505/3^5 = 2 19 19/3^4 = 0 19 19/3^3 = 0 19 19/3^2 = 2 1 1/3^1 = 0 1 1/3^0 = 1 0 The sequence of quotients, top down, form the entry in the table for 1234. Obviously this algorithm works for any N.

Examples

			The 4th concatenation of the integers > 0 is 1234. base(10,3,1234) = 1200201 the 4th entry in the table.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..195

Crossrefs

Cf. A007908, A050926, A097582, A097583.

Cf. A007089.

Programs

Mathematica

Table[FromDigits[IntegerDigits[FromDigits[Flatten[Table[ IntegerDigits[n],{n,i}]]],3]],{i,12}] (* Harvey P. Dale, May 23 2011 *)

Formula

a(n) = A007089(A007908(n)). - Seiichi Manyama, Apr 23 2022