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 A256786 Numbers which are divisible by prime(d) for all digits d in their decimal representation. 16
 12, 14, 42, 55, 154, 222, 228, 714, 1122, 1196, 1212, 1414, 2112, 2142, 2262, 3355, 4144, 4242, 5335, 5544, 5555, 6162, 9499, 11112, 11144, 11214, 11424, 11466, 11622, 11818, 11914, 12222, 12882, 14112, 15554, 16666, 21216, 21222, 21252, 21888, 22122, 22212 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are zerofree, cf. A052382; there is no term containing digits 1 and 3 simultaneously; a(n) contains at least one digit 1 iff a(n) is even, cf. A011531, A005843; a(n) contains at least one digit 2 iff a(n) mod 3 = 0, cf. A011532, A008585; a(n) contains at least one digit 3 iff a(n) mod 10 = 5, cf. A011533, A017329; 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 Cf. A000040, A005843, A008585, A011531, A011532, A011533, A017329, A020639, A052382, A256874-A256879, A256882-A256884, A256865-A256870. Sequence in context: A330197 A127401 A332876 * A337874 A337876 A058073 Adjacent sequences:  A256783 A256784 A256785 * A256787 A256788 A256789 KEYWORD nonn,base AUTHOR Eric Angelini and Reinhard Zumkeller, Apr 10 2015 STATUS approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)