This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A241746 #62 Feb 10 2024 18:52:53
%S A241746 23,103,163,223,283,343,403,463,523,583,643,703,763,823,883,943,1003,
%T A241746 1063,1123,1183,1243,1303,1363,1423,1483,1543,1603,1663,1723,1783,
%U A241746 1843,1903,1963,2023,2083,2143,2203,2263,2323,2383,2443,2503,2563,2623,2683,2743
%N A241746 Smallest number greater than n that CANNOT be scored using n darts on a standard dartboard.
%C A241746 It is assumed that each of the n darts scores. - _Colin Barker_, May 19 2014
%C A241746 Starting at a(2) = 103, each subsequent term is 60 plus the previous term. Proof: All numbers from 2 to 102 can be scored using 2 darts. For 3 darts, the possible totals are the set of sums of the numbers between 2 and 102 (the 2-dart combinations) and the values for the third dart (see A242718 for allowable scores). Since the 2-dart scores are continuous in the 2 - 102 range, any value less than 102 plus the maximum 1-dart total can be obtained by selecting the maximum 1-dart score (60) and then choosing the (desired score - 60) from the 2-dart combinations. For example, to score 95 with 3 darts, assume dart 1 scores 60 and then choose 35 from the 2-dart score list. Thus, the lowest score that cannot be obtained with 3 darts is 61 (the maximum 1-dart score + 1) + 102 (the maximum 2-dart score) = 163. Repeat this approach for subsequent terms. - _David Consiglio, Jr._, Jun 11 2014
%H A241746 Wikipedia, <a href="http://en.wikipedia.org/wiki/Darts">Darts</a>
%H A241746 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A241746 a(1) = 23, remaining terms: a(n) = 103 + 60*(n-2). - _David Consiglio, Jr._, Jun 11 2014
%F A241746 From _Jianing Song_, Jan 22 2021: (Start)
%F A241746 G.f.: 17 - 20*x + (77*x-17)/(1-x)^2.
%F A241746 E.g.f.: 17 - 20*x + (60*x-17)*exp(x). (End)
%e A241746 a(6) = 403. All numbers from 5 - 342 can be scored using 5 darts. Thus, 60 (dart 1) + 342 (remaining 5 darts) = 402 -> The maximum score for 6 darts. - _David Consiglio, Jr._, Jun 11 2014
%t A241746 Join[{23},NestList[60+#&,103,60]] (* _Harvey P. Dale_, Sep 18 2020 *)
%o A241746 (PARI) a(n) = 103 + 60*(n-2) - 20*!(n-1); \\ _Jinyuan Wang_, May 30 2021
%K A241746 nonn,easy
%O A241746 1,1
%A A241746 _John Bibby_, May 18 2014
%E A241746 a(2)-a(4) from _Colin Barker_, May 19 2014
%E A241746 a(5)-a(11) from _David Consiglio, Jr._, Jun 12 2014
%E A241746 More terms from _Harvey P. Dale_, Sep 18 2020