Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Feb 21 2014 03:17:02
%S 497375,539019,543447,586476,589629,601575,646479,858609,895688,959097
%N Numbers n such that the union of the decimal digits of n^2 and n^3 contains every decimal digit exactly three times.
%C The sequence is finite (proof in reference). There are exactly 10 numbers.
%D J.-M. De Koninck - Armel Mercier, 1001 problemes en theorie classique des nombres, exercise number 255, p. 184, Ellipses, Paris 2004.
%e 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".
%p 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):
%K nonn,base,fini,full
%O 1,1
%A _Michel Lagneau_, Jan 01 2011