A364751 Minimum sum of digits for any number of length n digits in fractional base 4/3.

0, 3, 5, 6, 6, 8, 8, 9, 10, 10, 11, 11, 11, 11, 13, 14, 16, 17, 17, 17, 18, 19, 21, 22, 22, 23, 24, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 29, 31, 33, 34, 35, 36, 37, 38, 38, 38, 39, 39, 41, 41, 42, 42, 43, 43, 45, 45, 46, 46, 48, 50, 50, 52, 52, 52, 52, 53, 55

Offset: 1

Author

Kevin Ryde, Sep 07 2023

Keywords

• nonn
• base

Comments

0 is taken to be 1 digit long so a(1) = 0.

Terms can be derived from A364779 by a(n) = s for the smallest s where k = A364779(s) is >= n digits long (noting that stripping trailing 0's from k suffices to show numbers with sum of digits s exist at each length down to where sum s-1 exists).

Links

• Kevin Ryde, Table of n, a(n) for n = 1..209
• Kevin Ryde, Mean Digit Plot
• Index entries for sequences related to fractional bases

Crossrefs

Cf. A024631 (base 4/3), A244041 (sum of digits), A364779 (largest with sum).

Cf. A363758 (maximum sum).

Formula

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