%I #34 May 09 2023 19:06:27

%S 13,19,25,26,35,38,47,49,50,52,55,67,70,76,94,95,97,98,100,103,104,

%T 109,110,115,117,131,134,140,151,152,157,159,171,175,179,183,185,187,

%U 188,190,193,194,196,199,200,203,206,208,217,218,220,227,229

%N Inconsummate numbers in base 2: no number is this multiple of the sum of its digits (in base 2).

%C Equivalently, these are the natural numbers that cannot be written as the arithmetic mean of distinct powers of 2. - _Brian Kell_, Feb 28 2009

%H Daniel Mondot, <a href="/A058898/b058898.txt">Table of n, a(n) for n = 1..33099</a>

%F n such that A065413(n) = 0. - _Brian Kell_, Mar 01 2009

%p For Maple code see A058906.

%t Do[k = n; While[ Apply[ Plus, IntegerDigits[k, 2] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]

%o (Python)

%o from itertools import count, islice, combinations_with_replacement

%o def A058898_gen(startvalue=1): # generator of terms >= startvalue

%o for n in count(max(startvalue,1)):

%o for l in count(1):

%o if l*n < 1<<l-1:

%o yield n

%o break

%o for d in combinations_with_replacement((0,1),l):

%o if (s:=sum(d))>0 and sorted(bin(s*n)[2:]) == [str(e) for e in d]:

%o break

%o else:

%o continue

%o break

%o A058898_list = list(islice(A058898_gen(),20)) # _Chai Wah Wu_, May 09 2023

%Y Cf. A003635, A052491, A058899-A058907.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Jan 09 2001