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 A069759 #17 Aug 15 2025 04:27:17
%S A069759 107,647,2159,5399,11339,21167,36287,58319,89099,130679,185327,255527,
%T A069759 343979,453599,587519,749087,941867,1169639,1436399,1746359,2103947,
%U A069759 2513807,2980799,3509999,4106699,4776407
%N A069759 Frobenius number of the numerical semigroup generated by consecutive hex numbers.
%C A069759 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 hex numbers 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 A069759 Harvey P. Dale, <a href="/A069759/b069759.txt">Table of n, a(n) for n = 1..1000</a>
%H A069759 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).
%H A069759 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A069759 a(n) = 9*n^4+36*n^3+45*n^2+18*n-1; with offset 2, a(n) = 9*n^4-9*n^2-1.
%F A069759 G.f.: x*(107+112*x-6*x^2+4*x^3-x^4)/(1-x)^5. - _Colin Barker_, Feb 14 2012
%e A069759 a(1)=107 because 107 is not a nonnegative linear combination of 7 and 19, but all integers greater than 107 are.
%t A069759 FrobeniusNumber/@Partition[Table[3n^2+3n+1,{n,30}],2,1] (* _Harvey P. Dale_, Dec 25 2018 *)
%Y A069759 Cf. A003215, A037165, A059769, A069755-A069764.
%K A069759 easy,nonn
%O A069759 1,1
%A A069759 Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 08 2002