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Search: id:A092175
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| A092175 |
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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. |
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1
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| 2, 3, 13, 29, 182, 427, 3931, 8185, 102781, 199991, 3179143, 5971957, 11418731, 210826995, 4754446861, 8589934577, 222195898594, 396718580719, 11575488191148, 20479999999981, 665306762187614, 1168636602822635
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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Michael Brand was the originator of the problem.
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LINKS
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IBM Corp., April 2004 "Ponder This" challenge.
IBM Corp., April 2004 "Ponder This" challenge.
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FORMULA
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When n is even, a(n)=2*n^(n/2)-n+1.
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EXAMPLE
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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.
John Fletcher gives the following treatment of the case of odd B in '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.
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CROSSREFS
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Cf. A062971.
Sequence in context: A029737 A105891 A106867 this_sequence A072997 A037428 A073688
Adjacent sequences: A092172 A092173 A092174 this_sequence A092176 A092177 A092178
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KEYWORD
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nonn
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AUTHOR
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Ken Bateman (kbateman(AT)erols.com) and Graeme McRae (g_m(AT)mcraefamily.com), Apr 01 2004
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), based on comments from Don Coppersmith and John Fletcher, May 11 2004
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