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a(2)=2; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
0

%I #28 Oct 10 2019 20:29:26

%S 2,19,172,1549,13942,125479,1129312,10163809,91474290,823268618,

%T 7409417569,66684758127,600162823149,5401465408346,48613188675118,

%U 437518698076066,3937668282684597,35439014544161376,318951130897452387,2870560178077071485,25835041602693643367,232515374424242790305,2092638369818185112747

%N a(2)=2; 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.

%C Appears to be (1/4) * #{ k < 10^n | 2k has no digit 0 }, at least up to n = 8. Has anyone a simple explanation for this? - _M. F. Hasler_, Oct 10 2019

%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]

%o (PARI) A224753_vec(N=30)=vector(N,n,N=if(n>1,A224752_nxt(N),2)) \\ _M. F. Hasler_, Oct 10 2019

%Y Cf. A224752-A224761.

%K nonn,base

%O 1,1

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