|
|
A330562
|
|
Positive numbers k with property that if d is any nonzero digit of k then k mod d is also a digit of k.
|
|
2
|
|
|
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 102, 103, 104, 105, 109, 110, 120, 130, 140, 150, 190, 200, 201, 202, 204, 206, 208, 210, 220, 230, 240, 250, 260, 280, 290, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Theorem: k must have a zero digit.
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.
|
|
LINKS
|
|
|
EXAMPLE
|
401 is a term since 401 mod 4 = 1 and 401 mod 1 = 0, and 1 and 0 are both digits of 401.
|
|
MATHEMATICA
|
Select[Range@ 600, Function[{k, d}, AllTrue[DeleteCases[d, 0], ! FreeQ[d, Mod[k, #]] &]] @@ {#, IntegerDigits[#]} &] (* Michael De Vlieger, Jan 01 2020 *)
|
|
PROG
|
(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
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|