A336748 a(n) is the smallest number that is the sum of at least n repdigits (not necessarily distinct) but not of any fewer.

1, 10, 21, 320, 2219, 32218, 332217, 3332216, 33332215, 333332214, 3333332213

Offset: 1

Author

Falcon Shapiro, Aug 02 2020

Keywords

• nonn
• base
• more

Comments

I believe the sequence is infinite.

a(10) exists and is <= 333332214.

Examples

			1      is the sum of 1 repdigit: 1;
10     is the sum of 2 repdigits: 9      + 1;
21     is the sum of 3 repdigits: 11     + 9     + 1;
320    is the sum of 4 repdigits: 222    + 88    + 9    + 1;
2219   is the sum of 5 repdigits: 1111   + 999   + 99   + 9   + 1;
32218  is the sum of 6 repdigits: 22222  + 8888  + 999  + 99  + 9  + 1;
332217 is the sum of 7 repdigits: 222222 + 99999 + 8888 + 999 + 99 + 9 + 1.
All numbers less than 10 can be summed with less than 2 repdigits.
All numbers less than 21 can be summed with less than 3 repdigits. etc.
		

Links

• Rémy Sigrist, C++ program

Crossrefs

Cf. A000325 (binary analog, see A100661), A010785.

Extensions

a(8) from Jinyuan Wang, Aug 03 2020

a(9) from David A. Corneth, Aug 03 2020

a(10)-a(11) from Rémy Sigrist, Aug 25 2022