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Search: id:A091766
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| A091766 |
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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. |
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+0
2
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| 1, 2, 6, 15, 25, 36, 48, 66, 86, 108, 136, 165, 197, 236, 279, 323, 368, 420, 473, 528, 584, 642, 701, 763, 832, 906, 981, 1057, 1134, 1212, 1302, 1396, 1491, 1587, 1685, 1788, 1892, 2004, 2117, 2232, 2348, 2466, 2585, 2705, 2829, 2954, 3081, 3220, 3365
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OFFSET
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0,2
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COMMENT
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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).
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.
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FORMULA
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For n > 2, a(n) = a(n-1)+A091767(n-1)+1. - David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2006
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EXAMPLE
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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.
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PROGRAM
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(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
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CROSSREFS
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Cf. A091767, A000244.
Sequence in context: A090979 A050508 A033298 this_sequence A138621 A033286 A098651
Adjacent sequences: A091763 A091764 A091765 this_sequence A091767 A091768 A091769
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 08 2004
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EXTENSIONS
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More terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 24 2006
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