A084906 Numbers with at least one place in their decimal representation to insert a division operator such that an integer results.

11, 21, 22, 31, 33, 41, 42, 44, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 101, 102, 105, 111, 121, 122, 123, 124, 126, 131, 141, 142, 147, 151, 153, 155, 161, 162, 164, 168, 171, 181, 182, 183, 186, 189, 191, 201, 202, 204, 205, 211, 213

Offset

1,1

Comments

A084904(a(n)) > 0; for all m = a(n) exists at least one k such that (m mod 10^k) > 0 and ((m/10^k) mod (m mod 10^k)) = 0.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

364 is a term, as 36/4=9; 365 is not a term, as 3/65 and 36/5 are not integers.

Mathematica

matchQ@l_:=MatchQ[l, {x__ /; (c = FromDigits@{x})>0, y__ /; (d = FromDigits@{y}) > 0 && Divisible[c, d]}]; Select[Range@2500, matchQ@IntegerDigits@# &] (* Hans Rudolf Widmer, Sep 08 2024 *)

Prog

(Python)
def ok(n):
    s = str(n)
    pairs = ((int(s[:i]), int(s[i:])) for i in range(1, len(s)))
    return any(c%d == 0 for c, d in pairs if d > 0)
print([k for k in range(214) if ok(k)]) # Michael S. Branicky, Nov 21 2021

Crossrefs

Cf. A084904, A084905.

Sequence in context: A279769 A084854 A108237 * A232184 A232185 A118853

Adjacent sequences: A084903 A084904 A084905 * A084907 A084908 A084909

Keyword

nonn,base

Author

Reinhard Zumkeller, Jun 10 2003

Status

approved