A357866 - OEIS

%I #10 Oct 21 2022 06:59:29

%S 0,0,1,0,2,0,3,2,4,2,5,2,6,4,7,4,8,4,9,6,10,6,11,6,12,8,13,8,14,8,15,

%T 10,16,10,17,10,18,12,19,12,20,12,21,14,22,14,23,14,24,16,25,16,26,16,

%U 27,18,28,18,29,18,30,20,31,20,32,20,33,22,34,22,35

%N a(n) is the greatest remainder of n divided by its sum of digits in any base > 1.

%e For n = 11, we have:

%e        b  sum of digits  remainder

%e     ----  -------------  ---------

%e        2              3          2

%e        3              3          2

%e        4              5          1

%e        5              3          2

%e        6              6          5

%e        7              5          1

%e        8              4          3

%e        9              3          2

%e       10              2          1

%e       11              1          0

%e     >=12             11          0

%e so a(11) = 5.

%o (PARI) a(n) = { my (mx=0); for (b=2, n, mx=max(mx, n%sumdigits(n, b))); return (mx); }

%o (Python)

%o from sympy.ntheory import digits

%o def a(n): return max((n%sum(digits(n, b)[1:]) for b in range(2, n+1)), default=0)

%o print([a(n) for n in range(1, 72)]) # _Michael S. Branicky_, Oct 17 2022

%Y Cf. A138530, A357823.

%K nonn,base

%O 1,5

%A _Rémy Sigrist_, Oct 17 2022