

A091766


For n > 2, let m be the least number that cannot be expressed as a(i), a(i)+a(j), or a(i)a(j) with i, j < n. Then a(n) = a(n1)+m.


1



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

0,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..48.


FORMULA

For n > 2, a(n) = a(n1) + A091767(n1) + 1.  David Wasserman, Apr 24 2006


EXAMPLE

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= 62), (5=61), (6), (7=6+1), (8=6+2) hence a(4) = 15 and 9 = 156.


PROG

(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, Apr 24 2006


CROSSREFS

Cf. A000244, A091767.
Sequence in context: A050508 A033298 A153274 * A269706 A293402 A192691
Adjacent sequences: A091763 A091764 A091765 * A091767 A091768 A091769


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Feb 08 2004


EXTENSIONS

More terms from David Wasserman, Apr 24 2006


STATUS

approved



