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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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

LINKS

Steve Butler, Table of n, a(n) for n = 1..500

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

Adjacent sequences:  A239273 A239274 A239275 * A239277 A239278 A239279

KEYWORD

nonn

AUTHOR

Steve Butler, Mar 13 2014

STATUS

approved

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Last modified March 8 08:16 EST 2021. Contains 341942 sequences. (Running on oeis4.)