A058898 Inconsummate numbers in base 2: no number is this multiple of the sum of its digits (in base 2).

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

Daniel Mondot, Table of n, a(n) for n = 1..33099

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

Cf. A003635, A052491, A058899-A058907.

Sequence in context: A109902 A214031 A250293 * A227092 A123840 A258589

Adjacent sequences: A058895 A058896 A058897 * A058899 A058900 A058901

Keyword

nonn,base

Author

N. J. A. Sloane, Jan 09 2001

Status

approved