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 A069757 #12 Aug 15 2025 04:26:07 %S A069757 43,133,287,1699,921,1569,3006,3197,4129,12915,6445,8621,14087,13549, %T A069757 16753,43144,20783,25793,38854,35769,43321,101747,48147,57764,82815, %U A069757 74393,89017,198120,93689,108983,151478,133957,159025,341659,162180 %N A069757 Frobenius number of the numerical semigroup generated by three consecutive pentagonal numbers. %C A069757 The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the greatest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since three consecutive pentagonal numbers are relatively prime, they generate a numerical semigroup with a Frobenius number. %H A069757 Harvey P. Dale, <a href="/A069757/b069757.txt">Table of n, a(n) for n = 2..1000</a> %H A069757 R. Fröberg, C. Gottlieb and R. Häggkvist, <a href="https://gdz.sub.uni-goettingen.de/id/PPN362162808_0035">On numerical semigroups</a>, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number). %e A069757 a(2)=43 because 43 is not a nonnegative linear combination of 5, 12 and 22, but all integers greater than 43 are. %t A069757 FrobeniusNumber/@Partition[PolygonalNumber[5,Range[2,40]],3,1] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 16 2018 *) %Y A069757 Cf. A000326, A037165, A059769, A069755-A069764. %K A069757 easy,nonn %O A069757 2,1 %A A069757 Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 05 2002