login
A239276
Smallest start for n consecutive numbers such that all the products of any two distinct numbers are distinct.
3
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, 100, 113, 121, 121, 145, 145, 172, 183, 211, 211, 211, 243, 256, 281, 289, 289, 326, 331, 346, 369, 385, 385, 426, 426, 443, 469, 487, 487, 533, 533, 581, 581, 601, 601
OFFSET
1,6
COMMENTS
a(n-1) <= a(n) <= n^2.
LINKS
EXAMPLE
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.)
MATHEMATICA
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 *)
PROG
(Sage)
def find_start(n):
q=1
while True:
L={}
advance=True
for i in range(n-1):
for j in range(i+1, n):
if (q+i)*(q+j) not in L:
L[(q+i)*(q+j)]=1
else:
advance=False
break
if not advance:
break
else:
return q
q+=1
CROSSREFS
Cf. A239277.
Sequence in context: A297838 A032360 A117150 * A284132 A263427 A052147
KEYWORD
nonn
AUTHOR
Steve Butler, Mar 13 2014
STATUS
approved