A097582 Base 7 representation of the concatenation of the first n numbers with the most significant digits first.

1, 15, 234, 3412, 50664, 1022634, 13331215, 206636142, 3026236221, 614636352655, 155123512633260, 35001313215554565, 10403265603212022112, 2132066345452131466644, 434014101450663623262042

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 7^p such that 7^p < N. Then p = [log(N)/log(7)] and for 0 <= qi <= 6 [N/7^p] = q1 + r1 [r1/7^(p-1)] = q2 + r2 ........................ rp/7^1 = qp + rp+1 rp+1/7^0 = qp+1 0 For N = 1234, p = [log(1234)/log(7)] = 3 division quot rem 1234/7^3 = 3 205 205/7^2 = 4 9 9/7^1 = 1 2 2/7^0 = 2 0 The sequence of quotients, top down, forms 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..318

Crossrefs

Cf. A007908, A050926, A097580, A097583.

Cf. A007093.

Formula

a(n) = A007093(A007908(n)). - Seiichi Manyama, Apr 23 2022