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

Author

N. J. A. Sloane, Jan 09 2001

Keywords

• nonn
• base

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

Crossrefs

Cf. A003635, A052491, A058899-A058907.

Programs

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} ]

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<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

Formula

n such that A065413(n) = 0. - Brian Kell, Mar 01 2009