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Integers which are exactly the concatenation of the first m even numbers (A019520) divided by their sum (A002378 = m^2+m).
2

%I #5 Nov 21 2013 12:47:50

%S 1,4,8227,3427918353

%N Integers which are exactly the concatenation of the first m even numbers (A019520) divided by their sum (A002378 = m^2+m).

%C A probability argument suggests that this sequence may be finite.

%e a(1) = 2/2 =1; a(2) = 24/(2+4) = 4; a(3) = 246810/(2+4+6+8+10) = 8227; a(4) = 246810121416/(2+4+6+8+10+12+14+16).

%t With[{eds=Range[2,1500,2]},Select[Table[FromDigits[Flatten[ IntegerDigits/@ Take[eds,n]]]/Total[Take[eds,n]],{n,502}],IntegerQ]] (* _Harvey P. Dale_, Nov 29 2011 *)

%Y Cf. A067121, A072723, A072725.

%K base,nonn

%O 1,2

%A _Henry Bottomley_, Jul 06 2002