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%I #24 Sep 08 2022 08:46:24
%S 10,20,30,40,50,60,70,80,90,100,101,102,103,104,105,109,110,120,130,
%T 140,150,190,200,201,202,204,206,208,210,220,230,240,250,260,280,290,
%U 300,301,302,303,306,309,310,320,330,360,390,400,401,402,404,408,420,440,460,480,500,501,502,504,505,510,520,540,550,590
%N Positive numbers k with property that if d is any nonzero digit of k then k mod d is also a digit of k.
%C Theorem: k must have a zero digit.
%C Proof: If not, let s be the smallest digit in k. Then d = (k mod s) is a digit of k, and d < s. Contradiction.
%C Pandigital numbers (A171102) are necessarily an infinite subset. - _Hans Havermann_, Jan 02 2020
%H Rémy Sigrist, <a href="/A330562/b330562.txt">Table of n, a(n) for n = 1..25000</a>
%e 401 is a term since 401 mod 4 = 1 and 401 mod 1 = 0, and 1 and 0 are both digits of 401.
%t Select[Range@ 600, Function[{k, d}, AllTrue[DeleteCases[d, 0], ! FreeQ[d, Mod[k, #]] &]] @@ {#, IntegerDigits[#]} &] (* _Michael De Vlieger_, Jan 01 2020 *)
%o (PARI) is(k) = my (d=Set(digits(k))); for (i=1, #d, if (d[i] && setsearch(d, k%d[i])==0, return (0))); return (1) \\ _Rémy Sigrist_, Jan 01 2020
%o (Magma) [k:k in [1..600]| forall{c:c in Set(Intseq(k)) diff {0}| k mod c in Intseq(k)}]; // _Marius A. Burtea_, Jan 01 2020
%Y Cf. A330563 (primes), A171102 (pandigital subset).
%K nonn,base
%O 1,1
%A _N. J. A. Sloane_, Dec 31 2019, following a suggestion from _Eric Angelini_
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