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

1,1

Links

Table of n, a(n) for n=1..50.

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} ]

Prog

(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

Crossrefs

Cf. A003635, A052491, A058898-A058907.

Sequence in context: A043862 A043871 A269987 * A130694 A269748 A153831

Adjacent sequences: A058903 A058904 A058905 * A058907 A058908 A058909

Keyword

nonn,base

Author

N. J. A. Sloane, Jan 09 2001

Status

approved