A380998 Largest k such that there are no two subsets of the k consecutive integers n..(n+k-1) with the same product.

0, 4, 5, 6, 7, 6, 8, 7, 9, 8, 9, 8, 8, 7, 9, 11, 11, 10, 11, 10, 11, 13, 12, 11, 11, 10, 9, 12, 13, 12, 13, 12, 11, 14, 13, 14, 15, 14, 13, 14, 14, 13, 12, 11, 15, 17, 16, 15, 16, 15, 14, 13, 13, 12, 11, 16, 18, 17, 16, 15, 17, 16, 15, 14, 13, 18, 17, 16, 15

Offset

1,2

Comments

For n >= 2, A239291(n) is the least k such that a(k) >= n. The reason that this does not hold for n = 1 is that the empty subset is not considered in A239291.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Michael S. Branicky, Python Program for OEIS A380998

Formula

a(n) >= a(n-1)-1.

Example

For n = 7, no two subsets of the 8 numbers 7..14 have the same product, but for the 9 numbers 7..15 the two subsets {8, 15} and {10, 12} have the same product (120), so a(7) = 8.
For n = 14, no two subsets of the 7 numbers 14..20 have the same product, but for the 8 numbers 14..21 the two subsets {14, 18, 20} and {15, 16, 21} have the same product (5040), so a(14) = 7.

Prog

(Python) # see linked program

Crossrefs

Cf. A239291, A380999, A381000.

Sequence in context: A334501 A114546 A385883 * A067471 A102691 A014553

Adjacent sequences: A380995 A380996 A380997 * A380999 A381000 A381001

Keyword

nonn

Author

Pontus von Brömssen, Feb 11 2025

Status

approved