A363758 Maximum sum of digits for any number with n digits in fractional base 4/3.

0, 3, 6, 8, 9, 12, 13, 15, 17, 19, 22, 24, 26, 28, 30, 32, 33, 36, 37, 40, 42, 44, 46, 48, 50, 52, 54, 56, 57, 60, 62, 65, 67, 70, 71, 73, 75, 77, 80, 83, 84, 87, 90, 93, 94, 96, 98, 101, 104, 106, 108, 109, 112, 115, 117, 120, 122, 123, 126, 129, 131, 133, 134

Offset: 0

Author

Kevin Ryde, Jun 20 2023

Keywords

• nonn
• base

Comments

This sequence is strictly increasing since if a(n) is attained by the sum of digits of k, then the final digit of k is 3 and (k - (k mod 3))*4/3 + 3 is the same digits with a new second-least significant 1, 2 or 3 inserted, and so a(n+1) >= a(n) + 1.

Terms can be derived from A357425 by a(n) = s for the largest s where A357425(s) has n digits in base 4/3.

Examples

			For n=9, the numbers with 9 digits in base 4/3 are 60 to 79 and among them the maximum sum of digits is A244041(75) = 19 (those digits being 321023323), and so a(9) = 19.
		

Links

• Kevin Ryde, Table of n, a(n) for n = 0..207
• Kevin Ryde, Mean Digit Plot (and LaTeX source).
• Index entries for sequences related to fractional bases

Crossrefs

Cf. A024631 (base 4/3), A244041 (sum of digits).

Cf. A357425 (smallest with sum s), A087192.

Formula

a(n) = Max_{4*A087192(n-1) <= i < 4*A087192(n)} A244041(i), for n>=2.