A174823 Numbers n such that the union of the decimal digits of n^2 and n^3 contains every decimal digit exactly three times.

497375, 539019, 543447, 586476, 589629, 601575, 646479, 858609, 895688, 959097

Offset

1,1

Comments

The sequence is finite (proof in reference). There are exactly 10 numbers.

References

J.-M. De Koninck - Armel Mercier, 1001 problemes en theorie classique des nombres, exercise number 255, p. 184, Ellipses, Paris 2004.

Links

Table of n, a(n) for n=1..10.

Example

497375 is in the sequence because: 497375^2 = 247381890625; 497375^3 = 123041567849609375; and the union of the digits is:{247381890625123041567849609375} contains 3 digits "0", 3 digits "1", 3 digits "2", ..., 3 digits "9".

Maple

with(numtheory): U:=array(1..30) :c:=0:for i from 300000 to 1000000 do: n2:=i^2:n3:=i^3:l2:=length(n2):l3:=length(n3):if  l2=30-l3 then n0:=n2:nn0:=n3:for m from 1 to l2 do:q2:=n0:u2:=irem(q2, 10):v2:=iquo(q2, 10):n0:=v2 : U[m]:=u2:od:for mm from l2+1 to 30 do:q3:=nn0:u3:=irem(q3, 10):v3:=iquo(q3, 10):nn0:=v3 : U[mm]:=u3: od: s1:=0:s2:=0:s3:=0:for j from 1 to 30 do:s1:=s1+U[j]^3:s2:=s2+U[j]^7:od:if  s1=6075 and s2=24241275 then c:=c+1:printf(`%d, `, i): else fi:else fi:od: print(c):

Crossrefs

Sequence in context: A082248 A166196 A237383 * A238152 A145539 A157759

Adjacent sequences: A174820 A174821 A174822 * A174824 A174825 A174826

Keyword

nonn,base,fini,full

Author

Michel Lagneau, Jan 01 2011

Status

approved