OFFSET
1,2
COMMENTS
This sequence is inspired by a problem, proposed by Argentina during the 39th International Mathematical Olympiad in 1998 at Taipei, Taiwan, but not used for the competition.
The problem asked for a proof that, for each positive integer n, there exists a n-digit number, not containing the digit 0 and that is divisible by the sum of its digits (see links: Diophante in French and Kalva in English).
This sequence lists the smallest such n-digit integer.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1000
Diophante, Bon souvenir de Buenos-Aires.
EXAMPLE
111114 has 6 digits, does not contain 0 and is divisible by 1+1+1+1+1+4 = 9 (111114 = 9*12346), while 111111, 111112, 111113 are not respectively divisible by sum of their digits: 6, 7, 8; hence, a(6) = 111114.
MATHEMATICA
hQ[n_] := ! MemberQ[(d = IntegerDigits[n]), 0] && Divisible[n, Plus @@ d]; a[n_] := Module[{k = (10^n - 1)/9}, While[! hQ[k], k++]; k]; Array[a, 30] (* Amiram Eldar, Oct 03 2021 *)
PROG
(PARI) a(n) = for(k=(10^n-1)/9, 10^n-1, if (vecmin(digits(k)) && !(k % sumdigits(k)), return (k))); \\ Michel Marcus, Oct 03 2021
(Python)
def niven(n):
s = str(n)
return '0' not in s and n%sum(map(int, s)) == 0
def a(n):
k = int("1"*n)
while not niven(k): k += 1
return k
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Oct 09 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Oct 03 2021
EXTENSIONS
More terms from Amiram Eldar, Oct 03 2021
STATUS
approved