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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.

Pandigital numbers (A171102) are necessarily an infinite subset. - Hans Havermann, Jan 02 2020

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..25000

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

Cf. A330563 (primes), A171102 (pandigital subset).

Sequence in context: A011540 A098394 A057169 * A328783 A201014 A096092

Adjacent sequences:  A330559 A330560 A330561 * A330563 A330564 A330565

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Dec 31 2019, following a suggestion from Eric Angelini

STATUS

approved

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Last modified September 22 21:06 EDT 2020. Contains 337291 sequences. (Running on oeis4.)