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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. 3
2, 3, 13, 29, 182, 427, 3931, 8185, 102781, 199991, 3179143, 5971957, 114818731, 210826995, 4754446861, 8589934577, 222195898594, 396718580719, 11575488191148, 20479999999981, 665306762187614, 1168636602822635, 41826814261329723, 73040694872113129 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
REFERENCES
Michael Brand was the originator of the problem.
LINKS
FORMULA
When n is even, a(n) = 2*n^(n/2) - n + 1.
EXAMPLE
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.
CROSSREFS
Cf. A062971.
Sequence in context: A215375 A233523 A256712 * A317898 A317187 A296291
KEYWORD
nonn,base
AUTHOR
Ken Bateman (kbateman(AT)erols.com) and Graeme McRae, Apr 01 2004
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
STATUS
approved

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Last modified July 16 05:19 EDT 2024. Contains 374343 sequences. (Running on oeis4.)