OFFSET
1,1
COMMENTS
All terms are zerofree, cf. A052382;
there is no term containing digits 1 and 3 simultaneously;
A020639(a(n)) <= 23.
The equivalent in base 2 is the empty sequence, in base 3 it is A191681\{0}; see A256874-A256879 for the base 4 - base 9 variant, and A256870 for a variant where digits 0 are allowed but divisibility by prime(d+1) is required instead. - M. F. Hasler, Apr 11 2015
LINKS
Lars Blomberg and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Éric Angelini, Divisibility by primes, SeqFan list, Apr 10 2015.
EXAMPLE
Smallest terms containing the nonzero decimal digits:
. d | prime(d) | n | a(n)
. ---+----------+--------------------------
. 1 | 2 | 1 | 12 = 2^2 * 3
. 2 | 3 | 1 | 12 = 2^2 * 3
. 3 | 5 | 16 | 3355 = 5 * 11 * 61
. 4 | 7 | 2 | 14 = 2 * 7
. 5 | 11 | 4 | 55 = 5 * 11
. 6 | 13 | 10 | 1196 = 2^2 * 13 * 23
. 7 | 17 | 8 | 714 = 2 * 3 * 7 * 17
. 8 | 19 | 7 | 228 = 2^2 * 3 * 19
. 9 | 23 | 10 | 1196 = 2^2 * 13 * 23 .
MATHEMATICA
Select[Range@22222, FreeQ[IntegerDigits[#], 0]&&Total[Mod[#, Prime[IntegerDigits[#]]]]==0&] (* Ivan N. Ianakiev, Apr 11 2015 *)
PROG
(Haskell)
a256786 n = a256786_list !! (n-1)
a256786_list = filter f a052382_list where
f x = g x where
g z = z == 0 || x `mod` a000040 d == 0 && g z'
where (z', d) = divMod z 10
(PARI) is_A256786(n)=!for(i=1, #d=Set(digits(n)), (!d[i]||n%prime(d[i]))&&return) \\ M. F. Hasler, Apr 11 2015
(Python)
primes = [1, 2, 3, 5, 7, 11, 13, 17, 19, 23]
def ok(n):
s = str(n)
return "0" not in s and all(n%primes[int(d)] == 0 for d in s)
print([k for k in range(22213) if ok(k)]) # Michael S. Branicky, Dec 14 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Reinhard Zumkeller, Apr 10 2015
STATUS
approved