A180622 Number of distinct sums i+j, absolute differences |i-j|, products ij and quotients i/j and j/i with 1 <= i, j <= n.

3, 6, 12, 19, 30, 38, 56, 68, 86, 100, 129, 143, 178, 197, 222, 246, 293, 313, 367, 392, 428, 460, 525, 551, 606, 643, 694, 730, 813, 841, 931, 977, 1034, 1084, 1151, 1188, 1296, 1351, 1419, 1467, 1586, 1627, 1752, 1811, 1880, 1947, 2084, 2132, 2247, 2308

Offset

1,1

Comments

I was inspired by the 24-game. How many results can you get from two numbers by addition, subtraction, multiplication and division?

Links

Owen Whitby, Table of n, a(n) for n = 1..2000

Example

For n = 3 sums 2, 3, 4, 5, 6 differences 0, 1, 2 multiplications 1, 2, 3, 4, 6, 9 divisions 1/2, 1/3, 2/3, 2, 3, 3/2 different results are 2, 3, 4, 5, 6, 0, 1, 9, 1/2, 1/3, 2/3, 3/2 or ordered 0, 1/3, 1/2, 2/3, 1, 3/2, 2, 3, 4, 5, 6, 9 so f(3) = 12.

Maple

A180622 := proc(n) s := {} ; for i from 1 to n do for j from 1 to n do s := s union {i+j} ; s := s union {abs(i-j)} ; s := s union {i*j} ; s := s union {i/j} ; s := s union {j/i} ; end do: end do: nops(s) ; end proc: seq(A180622(n), n=1..83) ; # R. J. Mathar, Sep 19 2010

Mathematica

a180622[maxn_] := Module[{seq = {}, vals = {}, vnew, an, n1}, Do[vnew = {}; n1 = n - 1; Do[vnew = vnew~Join~{i + n, n - i, i*n, i/n, n/i}, {i, n1}]; vnew = vnew~Join~{n + n, 0, n*n, 1}; vals = Union[vals, vnew]; an = Length[vals]; AppendTo[seq, an], {n, maxn}]; seq] (* Owen Whitby, Nov 03 2010 *)

Crossrefs

Sequence in context: A267591 A101423 A263511 * A125851 A351621 A209489

Adjacent sequences: A180619 A180620 A180621 * A180623 A180624 A180625

Keyword

nonn

Author

Hein van Winkel (hein65(AT)duizendknoop.com), Sep 12 2010

Extensions

More terms from R. J. Mathar, Sep 19 2010

Status

approved