A226467 Numbers in which each digit equals the product (mod 10) of the other digits.

1, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 199, 446, 464, 555, 644, 666, 919, 991, 1111, 1199, 1919, 1991, 2228, 2282, 2822, 2888, 3337, 3373, 3733, 3777, 4444, 4466, 4646, 4664, 5555, 6446, 6464, 6644, 6666, 7333, 7377, 7737, 7773, 8222, 8288, 8828, 8882

Offset

1,2

Comments

The repunit numbers > 0 (A002275) are in the sequence.

From Robert Israel, May 28 2014: (Start)

The possibilities for the digits are as follows:

only 1's: any number of digits;

only 5's or only 6's: any number of digits >= 2;

only 4's or only 9's: any even number of digits;

only 2's, only 3's, only 7's or only 8's: any number of digits == 2 mod 4;

even number of 4's and any number of 6's;

even number of 9's and any number of 1's;

m 2's and n 8's, or m 3's and n 7's, where m - n == 2 mod 4. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

464 is in the sequence because the digits 4,6,4 satisfy
  4 = (6*4) mod 10;
  6 = (4*4) mod 10;
  4 = (4*6) mod 10.

Maple

filter:= proc(n) local L;
L:= convert(n, base, 10);
if not member(convert(L, set), {{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {1, 9}, {2, 8}, {3, 7}, {4, 6}}) then return false fi;
andmap(t -> convert(subsop(t=1, L), `*`) mod 10 = L[t], [$1..nops(L)]);
end proc;
select(filter, [$1..10^5]); # Robert Israel, May 28 2014

Mathematica

Select[Range[10^4], IntegerDigits[#] == Mod[Times@@IntegerDigits[#]/IntegerDigits[#], 10]&]

Crossrefs

Cf. A002275.

Sequence in context: A352535 A113585 A071273 * A244394 A299792 A115853

Adjacent sequences: A226464 A226465 A226466 * A226468 A226469 A226470

Keyword

nonn,base

Author

Michel Lagneau, Jun 08 2013

Extensions

Edited by Jon E. Schoenfield, Sep 09 2017

Status

approved