Search: id:A069764
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%I A069764
%S A069764 89,773,3611,12179,33349,78889,167383,326471,595409,1027949,1695539,
%T A069764 2690843,4131581,6164689,8970799,12769039,17822153,24441941,32995019,
%U A069764 43908899,57678389
%N A069764 Frobenius number of the numerical semigroup generated by consecutive 
               octahedral numbers.
%C A069764 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 
               octahedral 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.
%D A069764 R. Froberg, C. Gottlieb and R. Haggkvist, "On numerical semigroups", 
               Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).
%F A069764 a(n)=((1/3)n(2n^2+1)-1)((1/3)(n+1)(2(n+1)^2+1)-1)-1
%e A069764 a(2)=89 because 89 is not a nonnegative linear combination of 6 and 19 
               (the second and third octahedral numbers), but all integers greater 
               than 89 are.
%Y A069764 Cf. A005900, A037165, A059769, A069755-A069763.
%Y A069764 Sequence in context: A136646 A142566 A063654 this_sequence A053580 A103548 
               A097155
%Y A069764 Adjacent sequences: A069761 A069762 A069763 this_sequence A069765 A069766 
               A069767
%K A069764 nonn
%O A069764 2,1
%A A069764 Victoria A Sapko (vsapko(AT)canes.gsw.edu), Apr 18 2002

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