A058906 Inconsummate numbers in base 11: no number is this multiple of the sum of its digits (in base 11).

68, 70, 79, 80, 82, 92, 104, 200, 202, 212, 214, 224, 225, 248, 260, 314, 320, 332, 380, 392, 452, 458, 464, 490, 502, 508, 512, 513, 514, 518, 520, 524, 530, 562, 568, 574, 578, 579, 580, 584, 585, 590, 592, 595, 598, 599, 622, 628, 634, 635

Offset: 1

Author

N. J. A. Sloane, Jan 09 2001

Keywords

• nonn
• base

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Programs

Maple

digitsum := proc (n,b) local i; add(i,i=convert(n,base,b)) end; b := 11:N := 43922; L := []: for n from 1 to N do k := digitsum(n,b): if (n mod k)=0 then L := [op(L), n/k] fi: od: M := []: for i from 1 to 1000 do if not(member(i,L)) then M := [op(M),i] fi od: lprint(M);

Mathematica

base = 11; Do[k = n; While[ Apply[ Plus, IntegerDigits[k, base] ]*n != k && k < 250n, k += n]; If[k == 250n, Print[n] ], {n, 1, 10^3} ]

Python

from itertools import count, islice, combinations_with_replacement
from sympy.ntheory import digits
def A058906_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        for l in count(1):
            if 10*l*n < 11**(l-1):
                yield n
                break
            for d in combinations_with_replacement(range(11),l):
                if (s:=sum(d)) > 0 and sorted(digits(s*n,11)[1:]) == list(d):
                    break
            else:
                continue
            break
A058906_list = list(islice(A058906_gen(),20)) # Chai Wah Wu, May 09 2023