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Smallest number of additive persistence n.
(Formerly M4683)
12

%I M4683 #29 May 08 2020 13:57:11

%S 0,10,19,199,19999999999999999999999

%N Smallest number of additive persistence n.

%C The next term a(5) is 1 followed by 2222222222222222222222 9's.

%D Meimaris Antonios, On the additive persistence of a number in base p, Preprint, 2015.

%D H. J. Hindin, The additive persistence of a number, J. Rec. Math., 7 (No. 2, 1974), 134-135.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/persistence.html">The persistence of a number</a>, J. Recreational Math., 6 (1973), 97-98.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AdditivePersistence.html">Additive Persistence.</a>

%F For n>1 a(n) = 2*10^((a(n-1)-1)/9)-1.

%t lst = {0, 10}; Do[AppendTo[lst, 2*10^((lst[[-1]] - 1)/9) - 1], {3}]; lst (* _Arkadiusz Wesolowski_, Oct 17 2012 *)

%t Join[{0},NestList[2*10^((#-1)/9)-1&,10,3]] (* _Harvey P. Dale_, May 08 2020 *)

%Y Cf. A003001, A031286, A045646.

%K nonn,base,nice

%O 0,2

%A _N. J. A. Sloane_