A304368 Numbers n with additive persistence = 3.

199, 289, 298, 379, 388, 397, 469, 478, 487, 496, 559, 568, 577, 586, 595, 649, 658, 667, 676, 685, 694, 739, 748, 757, 766, 775, 784, 793, 829, 838, 847, 856, 865, 874, 883, 892, 919, 928, 937, 946, 955, 964, 973, 982, 991, 1099, 1189, 1198, 1279, 1288, 1297

Offset: 1

Author

Jaroslav Krizek, May 11 2018

Keywords

• nonn
• base

Comments

First deviation from A166459 is at a(101); a(101) = 1999, A166459(101) = 2089.

Examples

			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
		

Links

• Eric Weisstein's World of Mathematics, Additive Persistence.

Crossrefs

Cf. A031286.

Cf. Numbers with additive persistence k: A304366 (k=1), A304367 (k=2), A304373 (k=4).

Programs

Mathematica

Select[Range@ 1300, Length@ FixedPointList[Total@ IntegerDigits@ # &, #] == 5 &] (* Michael De Vlieger, May 14 2018 *)

PARI

nb(n) = {my(nba = 0); while (n > 9, n = sumdigits(n); nba++); nba;}
isok(n) = nb(n) == 3; \\ Michel Marcus, May 13 2018

Formula

A031286(a(n)) = 3.