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A226467
Numbers in which each digit equals the product (mod 10) of the other digits.
1
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
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: A113585 A071273 A377948 * A244394 A299792 A115853
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Jun 08 2013
EXTENSIONS
Edited by Jon E. Schoenfield, Sep 09 2017
STATUS
approved