A381645 a(n) is the largest integer with distinct digits whose digital sum is n.

0, 10, 20, 210, 310, 410, 3210, 4210, 5210, 6210, 43210, 53210, 63210, 73210, 83210, 543210, 643210, 743210, 843210, 943210, 953210, 6543210, 7543210, 8543210, 9543210, 9643210, 9743210, 9843210, 76543210, 86543210, 96543210, 97543210, 98543210, 98643210, 98743210, 98753210, 876543210, 976543210, 986543210, 987543210, 987643210, 987653210, 987654210, 987654310, 987654320, 9876543210

Offset: 0

Author

Gonzalo Martínez, Mar 03 2025

Keywords

• nonn
• base
• fini
• full

Comments

Since all the terms in this list have distinct digits, the highest possible digit sum is that of the number 987654321, which is 45. Therefore, this list is finite and has 46 terms.

All terms == 0 (mod 10).

All terms are members of A009995.

Examples

			For n = 5, the integers with distinct digits whose digital sum is 5 are: 5, 14, 23, 32, 41, 50, 104, 140, 203, 230, 302, 320, 401 and 410, where the largest of them is 410. So, a(5) = 410.
		

Crossrefs

Cf. A007953, A009995, A227378.