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a(2)=9; 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 #11 Jun 10 2016 00:21:00

%S 9,89,809,7288,65598,590387,5313488,47821396,430392568,3873533115,

%T 34861798038,313756182345,2823805641107,25414250769965,

%U 228728256929687,2058554312367185,18526988811304666,166742899301741995,1500686093715677956,13506174843441101605,121555573590969914446,1094000162318729230015,9846001460868563070144,88614013147817067631304,797526118330353608681743,7177735064973182478135694

%N a(2)=9; 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