A364779 - OEIS

%I #28 Dec 19 2024 11:45:36

%S 0,1,2,4,5,8,16,17,32,44,80,256,257,344,460,464,620,1472,1964,2620,

%T 2624,3500,6224,8300,11068,11072,26240,34988,46652,262144,262145,

%U 349528,349529,466040,621392,828524,1104700,1532816,3633344,6459280,6459281,11483168,19616912

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

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

%C 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.

%C 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).

%H Kevin Ryde, <a href="/A364779/b364779.txt">Table of n, a(n) for n = 0..150</a>

%H Kevin Ryde, <a href="/A364779/a364779_2.c.txt">C Code</a>

%H <a href="/index/Ba#base_fractional">Index entries for sequences related to fractional bases</a>

%o (C) /* See links */

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

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

%K nonn,base

%O 0,3

%A _Kevin Ryde_, Aug 13 2023