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A058898
Inconsummate numbers in base 2: no number is this multiple of the sum of its digits (in base 2).
16
13, 19, 25, 26, 35, 38, 47, 49, 50, 52, 55, 67, 70, 76, 94, 95, 97, 98, 100, 103, 104, 109, 110, 115, 117, 131, 134, 140, 151, 152, 157, 159, 171, 175, 179, 183, 185, 187, 188, 190, 193, 194, 196, 199, 200, 203, 206, 208, 217, 218, 220, 227, 229
OFFSET
1,1
COMMENTS
Equivalently, these are the natural numbers that cannot be written as the arithmetic mean of distinct powers of 2. - Brian Kell, Feb 28 2009
LINKS
FORMULA
n such that A065413(n) = 0. - Brian Kell, Mar 01 2009
MAPLE
For Maple code see A058906.
MATHEMATICA
Do[k = n; While[ Apply[ Plus, IntegerDigits[k, 2] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]
PROG
(Python)
from itertools import count, islice, combinations_with_replacement
def A058898_gen(startvalue=1): # generator of terms >= startvalue
for n in count(max(startvalue, 1)):
for l in count(1):
if l*n < 1<<l-1:
yield n
break
for d in combinations_with_replacement((0, 1), l):
if (s:=sum(d))>0 and sorted(bin(s*n)[2:]) == [str(e) for e in d]:
break
else:
continue
break
A058898_list = list(islice(A058898_gen(), 20)) # Chai Wah Wu, May 09 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jan 09 2001
STATUS
approved