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Numbers in which each digit equals the product (mod 10) of the other digits.
1

%I #16 Sep 09 2017 22:34:42

%S 1,11,22,33,44,55,66,77,88,99,111,199,446,464,555,644,666,919,991,

%T 1111,1199,1919,1991,2228,2282,2822,2888,3337,3373,3733,3777,4444,

%U 4466,4646,4664,5555,6446,6464,6644,6666,7333,7377,7737,7773,8222,8288,8828,8882

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

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

%C From _Robert Israel_, May 28 2014: (Start)

%C The possibilities for the digits are as follows:

%C only 1's: any number of digits;

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

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

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

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

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

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

%H Robert Israel, <a href="/A226467/b226467.txt">Table of n, a(n) for n = 1..10000</a>

%e 464 is in the sequence because the digits 4,6,4 satisfy

%e 4 = (6*4) mod 10;

%e 6 = (4*4) mod 10;

%e 4 = (4*6) mod 10.

%p filter:= proc(n) local L;

%p L:= convert(n,base,10);

%p 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;

%p andmap(t -> convert(subsop(t=1,L),`*`) mod 10 = L[t], [$1..nops(L)]);

%p end proc;

%p select(filter, [$1..10^5]); # _Robert Israel_, May 28 2014

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

%Y Cf. A002275.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, Jun 08 2013

%E Edited by _Jon E. Schoenfield_, Sep 09 2017