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A058900 Inconsummate numbers in base 4: no number is this multiple of the sum of its digits (in base 4).

%I A058900 #19 May 10 2023 12:18:22
%S A058900 29,41,71,83,93,111,113,114,116,117,122,123,125,135,137,143,146,153,
%T A058900 164,167,191,197,201,237,242,263,275,279,282,284,285,291,303,305,311,
%U A058900 323,326,327,332,359,362,369,372,375,377,382,383,389,407,410
%N A058900 Inconsummate numbers in base 4: no number is this multiple of the sum of its digits (in base 4).
%H A058900 Daniel Mondot, <a href="/A058900/b058900.txt">Table of n, a(n) for n = 1..15650</a>
%p A058900 For Maple code see A058906.
%o A058900 (Python)
%o A058900 from itertools import count, islice, combinations_with_replacement
%o A058900 from sympy.ntheory import digits
%o A058900 def A058900_gen(startvalue=1): # generator of terms >= startvalue
%o A058900     for n in count(max(startvalue,1)):
%o A058900         for l in count(1):
%o A058900             if 3*l*n < 1<<((l-1)<<1):
%o A058900                 yield n
%o A058900                 break
%o A058900             for d in combinations_with_replacement((0,1,2,3),l):
%o A058900                 if (s:=sum(d)) > 0 and sorted(digits(s*n,4)[1:]) == list(d):
%o A058900                     break
%o A058900             else:
%o A058900                 continue
%o A058900             break
%o A058900 A058900_list = list(islice(A058900_gen(),20)) # _Chai Wah Wu_, May 10 2023
%Y A058900 Cf. A003635, A052491, A058898-A058907.
%K A058900 nonn,base
%O A058900 1,1
%A A058900 _N. J. A. Sloane_, Jan 09 2001