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

14979, 19167, 19497, 19839, 20247, 20499, 21657, 21864, 22185, 22227, 22329, 25299, 25755, 26325, 28344, 28665, 29643, 32184, 32319, 32418, 32724, 32889, 34194, 34692, 35265, 35853, 36489, 36957, 39588, 41754, 42327, 42564, 42723, 43476, 43656, 44382, 44445

Offset

1,1

Comments

There are exactly 141 such numbers, no one of them being prime.

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

Links

Jinyuan Wang, Table of n, a(n) for n = 1..141

Example

20247 is in the sequence because 20247*74202 = 1502367894 contains ten different digits;
451410 is in the sequence because 451410*14154 = 6389257140 contains ten different digits.

Maple

with(numtheory): U:=array(1..50) :c:=0:for i from 5000 to 1000000 do: s1:=0:ll:=length(i):for
  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
  : U[m]:=u:od: B:={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}: A:=convert(U, set):z:=nops(A):else fi:
  if A intersect B = B and z=10 and l=10 then c:=c+1:printf(`%d, `, i): else fi:od:
  print(c):

Crossrefs

Cf. A054038, A156977.

Sequence in context: A203404 A236352 A064968 * A145275 A234654 A064730

Adjacent sequences: A178926 A178927 A178928 * A178930 A178931 A178932

Keyword

nonn,base,fini,full

Author

Michel Lagneau, Dec 30 2010

Extensions

Confirmed terms 14979-45765 and also that there are exactly 141 terms. - John W. Layman, Dec 30 2010

Status

approved