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A178929 Numbers m such that m*reversal(m) contains every decimal digit exactly once. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 19:43 EDT 2021. Contains 347617 sequences. (Running on oeis4.)