Search: id:A091766
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%I A091766
%S A091766 1,2,6,15,25,36,48,66,86,108,136,165,197,236,279,323,368,420,473,528,
%T A091766 584,642,701,763,832,906,981,1057,1134,1212,1302,1396,1491,1587,1685,
%U A091766 1788,1892,2004,2117,2232,2348,2466,2585,2705,2829,2954,3081,3220,3365
%N A091766 For n > 2, let m be the least number that can not be expressed as a(i), 
               a(i)+a(j), or a(i)-a(j) with i, j < n. Then a(n) = a(n-1)+m.
%C A091766 This can be treated as sequence of weights, one each of distinct denominations, 
               so that any value of weight r units can be measured using at most 
               two weights placing them in either side of the balance. e.g. 19 = 
               25-6 = a(5)-a(3).
%C A091766 n = x*a(k) +y*a(m), where x and y can take values -1, 0 or 1 has a solution. 
               Sequence A000244 gives sequence of weights with no restriction on 
               the number of weights.
%F A091766 For n > 2, a(n) = a(n-1)+A091767(n-1)+1. - David Wasserman (dwasserm(AT)earthlink.net), 
               Apr 24 2006
%e A091766 Using first three terms 1,2 and 6 all numbers up to 8 can be obtained 
               in this manner. (1), (2), (3=1+2), (4= 6-2), (5=6-1), (6), (7=6+1), 
               (8=6+2) hence a(4) = 15 and 9 = 15-6.
%o A091766 (PARI) A = vector(100); A[1] = 1; v = A; A[2] = 2; made = vector(50000); 
               x = 4; for (n = 3, 100, A[n] = A[n - 1] + x; made[A[n]] = 1; for 
               (i = 1, n - 1, made[A[n] - A[i]] = 1; made[A[n] + A[i]] = 1); while 
               (made[x], x++)); print(A) - David Wasserman (dwasserm(AT)earthlink.net), 
               Apr 24 2006
%Y A091766 Cf. A091767, A000244.
%Y A091766 Sequence in context: A050508 A033298 A153274 this_sequence A138621 A163061 
               A033286
%Y A091766 Adjacent sequences: A091763 A091764 A091765 this_sequence A091767 A091768 
               A091769
%K A091766 nonn
%O A091766 0,2
%A A091766 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 08 2004
%E A091766 More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2006

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