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

Author

Michel Lagneau, Dec 30 2010

Keywords

• nonn
• base
• fini
• full

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A054038, A156977.

Programs

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):

Extensions

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