A092175 Define d(n,k) to be the number of '1' digits required to write out all the integers from 1 through k in base n. E.g., d(10,9) = 1 (just '1'), d(10,10) = 2 ('1' and '10'), d(10,11) = 4 ('1', '10' and '11'). Then a(n) is the first k >= 1 such that d(n,k) > k.

2, 3, 13, 29, 182, 427, 3931, 8185, 102781, 199991, 3179143, 5971957, 114818731, 210826995, 4754446861, 8589934577, 222195898594, 396718580719, 11575488191148, 20479999999981, 665306762187614, 1168636602822635, 41826814261329723, 73040694872113129

Offset: 1

Author

Ken Bateman (kbateman(AT)erols.com) and Graeme McRae, Apr 01 2004

Keywords

• nonn
• base

Comments

The number of video tapes you can label sequentially starting with "1" using the n different number stickers that come in the box, working in base n.

Adapted from puzzle described in the Ponder This web page.

Examples

			John Fletcher gives the following treatment of the case of odd B at the 'solutions' link: a(10)=199991 because you can label 199990 tapes using 199990 sets of base-10 sticky digit labels, but the 199991st tape can't be labeled with 199991 sets of sticky digit labels.
		

References

• Michael Brand was the originator of the problem.

Links

• Gregory Marton, Table of n, a(n) for n = 1..100
• IBM Corp., April 2004 "Ponder This" challenge.
• IBM Corp., April 2004 "Ponder This" solutions.

Crossrefs

Cf. A062971.

Formula

When n is even, a(n) = 2*n^(n/2) - n + 1.

Extensions

Edited by Robert G. Wilson v, based on comments from Don Coppersmith and John Fletcher, May 11 2004

a(13) corrected and a(23) onwards added by Gregory Marton, Jul 29 2023