A239277 Smallest start for n consecutive numbers such that the product of any two numbers is unique.

1, 1, 1, 2, 3, 5, 5, 7, 11, 13, 13, 22, 22, 26, 33, 37, 37, 51, 51, 57, 67, 73, 73, 92, 92, 113, 113, 122, 145, 145, 145, 172, 183, 211, 211, 211, 243, 261, 281, 290, 295, 326, 331, 346, 369, 385, 385, 426, 426, 443, 469, 487, 487, 533, 533, 581, 581, 601, 601

Offset

1,4

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Example

For n=4 we have a(n)=2; 1 is impossible because 1*4=2*2; on the other hand the products of any two numbers from 2,3,4,5 are 4,6,8,9,10,12,15,16,20,25, which are all distinct.

Prog

(Sage)
def find_start(n):
    q=1
    while True:
        L={}
        advance=True
        for i in range(n-1):
            for j in range(i, 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. A239276.

Sequence in context: A120724 A117530 A238256 * A302445 A094749 A096539

Adjacent sequences: A239274 A239275 A239276 * A239278 A239279 A239280

Keyword

nonn

Author

Steve Butler, Mar 13 2014

Status

approved