A364779 Largest integer with sum of digits n in fractional base 4/3.

0, 1, 2, 4, 5, 8, 16, 17, 32, 44, 80, 256, 257, 344, 460, 464, 620, 1472, 1964, 2620, 2624, 3500, 6224, 8300, 11068, 11072, 26240, 34988, 46652, 262144, 262145, 349528, 349529, 466040, 621392, 828524, 1104700, 1532816, 3633344, 6459280, 6459281, 11483168, 19616912

Offset: 0

Author

Kevin Ryde, Aug 13 2023

Keywords

• nonn
• base

Comments

A largest integer exists since only a finite number of trailing 0 digits are possible, since each is a factor 4/3.

Each term k >= 3 has final digit d = k mod 4 which is always d < r where r = k mod 3 (and hence d = 0 or 1), since otherwise (k - r)*4/3 + r would split d into two final digits {d-r, r} for a larger number with the same sum of digits.

This sequence is strictly increasing since final digit d = 0 or 1 (and also a(2) = 2) can be incremented so that a(n)+1 is a candidate value for a(n+1).

Links

• Kevin Ryde, Table of n, a(n) for n = 0..150
• Kevin Ryde, C Code
• Index entries for sequences related to fractional bases

Crossrefs

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

Cf. A357425 (smallest of sum), A364780 (count by sum).

Programs

C

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