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a(2)=3; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
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%I #16 Jun 10 2016 00:21:00

%S 3,29,263,2369,21323,191908,1727173,15544558,139901023,1259109208,

%T 11331982873,101987845858,917890612731,8261015514587,74349139631290,

%U 669142256681616,6022280310134550,54200522791210955,487804705120898599,4390242346088087395

%N a(2)=3; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).

%C The sequence is infinite: a(n) always exists.

%C For computer programs and examples see A224752.

%D Eric Angelini, Postings to the Sequence Fans Mailing List, Apr 13 2013

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/MagicalSum.htm">Magic Sums</a>

%H E. Angelini, <a href="/A224752/a224752.pdf">Magic Sums</a> [Cached copy, with permission]

%Y Cf. A224752-A224761.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Apr 21 2013