A354854 Smallest number of powers of n with positive exponents that sum to a factorial.

1, 1, 2, 3, 8, 1, 12, 3, 16, 3, 30, 2, 48, 20, 6, 15, 80, 6, 108, 6, 20, 63, 176, 1, 24, 50, 50, 18

Offset

1,3

Comments

For n > 1, a(n) is the smallest base-n digit sum of m! for m >= A002034(n). Values m = A002034(n) correspond to A354861, and so a(n) <= A354861(n). The two sequences share many terms but differ: a(14) = 20 < 22 = A354861(14).

The sequence likely continues as 280, 4, 330, ...

Links

Table of n, a(n) for n=1..28.

Example

a(7) = 12 since 7! = 2*7^4 + 4*7^2 + 6*7^1 with 2+4+6=12, and the sum of 11 or less powers of 7 cannot be a multiple of 48.

Crossrefs

Cf. A000142, A002034, A354861.

Sequence in context: A138180 A345093 A079585 * A354861 A348261 A252651

Adjacent sequences: A354851 A354852 A354853 * A354855 A354856 A354857

Keyword

nonn,hard,more

Author

Max Alekseyev, Jun 08 2022

Extensions

a(17)-a(18) from Jinyuan Wang, Jun 10 2022

a(19)-a(28) from Max Alekseyev, Feb 01 2024

Status

approved