A006050 Smallest number of additive persistence n.

0, 10, 19, 199, 19999999999999999999999

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• nice

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.

Crossrefs

Cf. A003001, A031286, A045646.

Programs

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 *)

Formula

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