cp's OEIS Frontend

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.

%I A092175 #22 Dec 02 2024 16:29:33
%S A092175 2,3,13,29,182,427,3931,8185,102781,199991,3179143,5971957,114818731,
%T A092175 210826995,4754446861,8589934577,222195898594,396718580719,
%U A092175 11575488191148,20479999999981,665306762187614,1168636602822635,41826814261329723,73040694872113129
%N 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.
%C A092175 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.
%C A092175 Adapted from puzzle described in the Ponder This web page.
%D A092175 Michael Brand was the originator of the problem.
%H A092175 Gregory Marton, <a href="/A092175/b092175.txt">Table of n, a(n) for n = 1..100</a>
%H A092175 IBM Corp., <a href="https://research.ibm.com/haifa/ponderthis/challenges/April2004.html">April 2004 "Ponder This" challenge</a>.
%H A092175 IBM Corp., <a href="https://research.ibm.com/haifa/ponderthis/solutions/April2004.html">April 2004 "Ponder This" solutions</a>.
%F A092175 When n is even, a(n) = 2*n^(n/2) - n + 1.
%e A092175 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.
%Y A092175 Cf. A062971.
%K A092175 nonn,base
%O A092175 1,1
%A A092175 Ken Bateman (kbateman(AT)erols.com) and _Graeme McRae_, Apr 01 2004
%E A092175 Edited by _Robert G. Wilson v_, based on comments from Don Coppersmith and John Fletcher, May 11 2004
%E A092175 a(13) corrected and a(23) onwards added by _Gregory Marton_, Jul 29 2023