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A178929 Numbers m such that m*reversal(m) contains every decimal digit exactly once.

%I A178929 #21 Aug 04 2020 11:53:50
%S A178929 14979,19167,19497,19839,20247,20499,21657,21864,22185,22227,22329,
%T A178929 25299,25755,26325,28344,28665,29643,32184,32319,32418,32724,32889,
%U A178929 34194,34692,35265,35853,36489,36957,39588,41754,42327,42564,42723,43476,43656,44382,44445
%N A178929 Numbers m such that m*reversal(m) contains every decimal digit exactly once.
%C A178929 There are exactly 141 such numbers, no one of them being prime.
%C A178929 The sequence contains 15 semiprimes: 14979 = 3 * 4993, 19167 = 3 * 6389, 20499 = 3 * 6833, 21657 = 3 * 7219, 36489 = 3 * 12163,..., 98337 = 3 * 32779, and 98823 = 3*32941. - _Jonathan Vos Post_, Dec 31 2010
%H A178929 Jinyuan Wang, <a href="/A178929/b178929.txt">Table of n, a(n) for n = 1..141</a>
%e A178929 20247 is in the sequence because 20247*74202 = 1502367894 contains ten different digits;
%e A178929 451410 is in the sequence because 451410*14154 = 6389257140 contains ten different digits.
%p A178929 with(numtheory): U:=array(1..50) :c:=0:for i from 5000 to 1000000 do: s1:=0:ll:=length(i):for
%p A178929   q from 0 to ll do:x:=iquo(i, 10^q):y:=irem(x, 10):s1:=s1+y*10^(ll-1-q): od:n:=i*s1:l:=length(n):if   l=10 then n0:=n:s:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v
%p A178929   : U[m]:=u:od: B:={0,1,2,3,4,5,6,7,8,9}: A:=convert(U,set):z:=nops(A):else fi:
%p A178929   if A intersect B = B and z=10 and l=10 then c:=c+1:printf(`%d, `,i): else fi:od:
%p A178929   print(c):
%Y A178929 Cf. A054038, A156977.
%K A178929 nonn,base,fini,full
%O A178929 1,1
%A A178929 _Michel Lagneau_, Dec 30 2010
%E A178929 Confirmed terms 14979-45765 and also that there are exactly 141 terms. - _John W. Layman_, Dec 30 2010