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URL: https://oeis.org/A006050

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A006050
Smallest number of additive persistence n.
13
0, 10, 19, 199, 19999999999999999999999
OFFSET
0,2
COMMENTS
The next term a(5) is 1 followed by 2222222222222222222222 9's.
REFERENCES
Meimaris Antonios, On the additive persistence of a number in base p, Preprint, 2015.
H. J. Hindin, The additive persistence of a number, J. Rec. Math., 7 (No. 2, 1974), 134-135.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Shyam Sunder Gupta, Digital Root Wonders, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 1, 1-28.
N. J. A. Sloane, The persistence of a number, J. Recreational Math., 6 (1973), 97-98.
Eric Weisstein's World of Mathematics, Additive Persistence.
FORMULA
For n>1 a(n) = 2*10^((a(n-1)-1)/9)-1.
For n>1 a(n) is the number formed from the digit 1 and (a(n-1)-1)/9 digits 9. - Robert FERREOL, Sep 29 2025
MATHEMATICA
lst = {0, 10}; Do[AppendTo[lst, 2*10^((lst[[-1]] - 1)/9) - 1], {3}]; lst (* Arkadiusz Wesolowski, Oct 17 2012 *)
Join[{0}, NestList[2*10^((#-1)/9)-1&, 10, 3]] (* Harvey P. Dale, May 08 2020 *)
CROSSREFS
KEYWORD
nonn,base,nice
STATUS
approved