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%I #15 May 28 2018 10:37:41
%S 199,289,298,379,388,397,469,478,487,496,559,568,577,586,595,649,658,
%T 667,676,685,694,739,748,757,766,775,784,793,829,838,847,856,865,874,
%U 883,892,919,928,937,946,955,964,973,982,991,1099,1189,1198,1279,1288,1297
%N Numbers n with additive persistence = 3.
%C First deviation from A166459 is at a(101); a(101) = 1999, A166459(101) = 2089.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AdditivePersistence.html">Additive Persistence.</a>
%F A031286(a(n)) = 3.
%e Repeatedly taking the sum of digits starting with 199 gives 19, 10, and then 1. There are three steps, so the additive persistence is 3, and 199 is a member. - _Michael B. Porter_, May 16 2018
%t Select[Range@ 1300, Length@ FixedPointList[Total@ IntegerDigits@ # &, #] == 5 &] (* _Michael De Vlieger_, May 14 2018 *)
%o (PARI) nb(n) = {my(nba = 0); while (n > 9, n = sumdigits(n); nba++); nba;}
%o isok(n) = nb(n) == 3; \\ _Michel Marcus_, May 13 2018
%Y Cf. A031286.
%Y Cf. Numbers with additive persistence k: A304366 (k=1), A304367 (k=2), A304373 (k=4).
%K nonn,base
%O 1,1
%A _Jaroslav Krizek_, May 11 2018
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