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

1,2

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.

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A007908, A050926, A097582, A097583.

Cf. A007089.

Sequence in context: A267867 A267889 A285696 * A216786 A350320 A295444

Adjacent sequences: A097577 A097578 A097579 * A097581 A097582 A097583

Keyword

base,nonn

Author

Cino Hilliard, Aug 29 2004

Status

approved