The On-Line Encyclopedia of Integer Sequences (OEIS)

A375071 revision #14

A375071

Smallest k such that Product_{i=1..k} (n+i) divides Product_{i=1..k} (n+k+i), or 0 if there is no such k.

5, 4, 207, 206, 2475, 984, 8171, 8170, 45144, 45143

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OFFSET

1,1

COMMENTS

Erdős and Straus asked if a(n) exists for all n.

a(10) = 45143 found by Bhavik Mechta, 2024.

LINKS

Thomas Bloom, Problem 389.

EXAMPLE

3*4*5*6 ∣ 7*8*9*10, so a(2) = 4.

PROG

(PARI) for(n=3, 10, for(k=1, 10000, if(prod(i=1, k, n+k+i)%prod(i=1, k, n+i)==0, print(n, " ", k); break)))

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

Ralf Stephan, Jul 29 2024

STATUS

proposed