cp's OEIS Frontend

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.

A069763 Frobenius number of the numerical semigroup generated by consecutive cubes.

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%I A069763 #19 Feb 12 2021 04:51:19
%S A069763 181,1637,7811,26659,73529,174761,372007,727271,1328669,2296909,
%T A069763 3792491,6023627,9254881,13816529,20114639,28641871,39988997,54857141,
%U A069763 74070739,98591219,129531401,168170617,215970551,274591799,345911149
%N A069763 Frobenius number of the numerical semigroup generated by consecutive cubes.
%C A069763 The Frobenius number of a numerical semigroup generated by relatively prime integers a_1,...,a_n is the largest positive integer that is not a nonnegative linear combination of a_1,...,a_n. Since consecutive cubes are relatively prime, they generate a numerical semigroup with a Frobenius number. The Frobenius number of a 2-generated semigroup <a,b> has the formula ab-a-b.
%H A069763 R. Fröberg, C. Gottlieb and R. Häggkvist, <a href="https://www.researchgate.net/publication/226359613_On_numerical_semigroups">On numerical semigroups</a>, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
%F A069763 a(n) = n^3*(n+1)^3-n^3-(n+1)^3 = n^6+3*n^5+3*n^4-n^3-3*n^2-3*n-1.
%F A069763 G.f.: x^2*(181+370*x+153*x^2+24*x^3-13*x^4+6*x^5-x^6)/(1-x)^7. [_Colin Barker_, Feb 14 2012]
%e A069763 a(2)=181 because 181 is not a nonnegative linear combination of 8 and 27, but all integers greater than 181 are.
%Y A069763 Cf. A000578, A037165, A059769, A069755-A069764.
%K A069763 easy,nonn
%O A069763 2,1
%A A069763 Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002