A239276 - OEIS

%I #29 Mar 14 2020 17:22:25

%S 1,1,1,1,1,4,5,7,9,13,13,22,22,25,25,37,37,51,51,57,67,73,73,92,92,

%T 100,113,121,121,145,145,172,183,211,211,211,243,256,281,289,289,326,

%U 331,346,369,385,385,426,426,443,469,487,487,533,533,581,581,601,601

%N Smallest start for n consecutive numbers such that all the products of any two distinct numbers are distinct.

%C a(n-1) <= a(n) <= n^2.

%H Steve Butler, <a href="/A239276/b239276.txt">Table of n, a(n) for n = 1..500</a>

%e For n=6 we have a(n)=4; 1 is impossible because 1*6=2*3, 2 is impossible because 2*6=3*4, and 3 is impossible because 3*8=4*6; however, the products of pairs of distinct numbers from {4,5,6,7,8,9}, i.e., 20,24,28,30,32,35,36,40,42,45,48,54,56,63,72, are all distinct. (Note that we do not count 6*6=4*9 since 6*6 does not involve distinct terms.)

%t a[1]=1; a[n_] := a[n] = Block[{k = a[n-1]}, While[Min@ Differences@ Sort[Times @@@ Subsets[Range[k, n+k-1], {2}]] == 0, k++]; k]; Array[a, 60] (* _Giovanni Resta_, Mar 14 2014 *)

%o (Sage)

%o def find_start(n):

%o     q=1

%o     while True:

%o         L={}

%o         advance=True

%o         for i in range(n-1):

%o             for j in range(i+1,n):

%o                 if (q+i)*(q+j) not in L:

%o                     L[(q+i)*(q+j)]=1

%o                 else:

%o                     advance=False

%o                     break

%o             if not advance:

%o                 break

%o         else:

%o             return q

%o         q+=1

%Y Cf. A239277.

%K nonn

%O 1,6

%A _Steve Butler_, Mar 13 2014