A309242 a(n) is the smallest integer m such that the equality Product_{i=1..n} (x_i + m) = (m+n)!/m! for integers x_1, ..., x_n from N = { 1, 2, ..., n } guarantees that they form a permutation of N.

0, 0, 0, 1, 2, 5, 6, 9, 10, 16, 18, 27, 28, 33, 45, 45, 45, 56, 78, 81, 108, 120, 136, 140, 180, 180, 192, 209, 210, 280, 280, 286, 325, 325, 380, 392, 527, 527, 527, 625, 650, 650, 703, 703

Offset

1,5

Comments

a(n) <= A065048(n) + 1.

Links

Table of n, a(n) for n=1..44.

JPF et al., A necessary and sufficient condition for (x_1,...,x_n) to be a permutation of (1,...,n). MathOverflow, 2019.

Crossrefs

Sequence in context: A213730 A191172 A078632 * A122701 A032925 A244749

Adjacent sequences: A309239 A309240 A309241 * A309243 A309244 A309245

Keyword

nonn,more

Author

Max Alekseyev, Jul 17 2019

Status

approved