A304366 Numbers with additive persistence = 1.

10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116

Offset: 1

Author

Jaroslav Krizek, May 11 2018

Keywords

• nonn
• base

Comments

For d >= 2, there are A000581(d+8) terms with d digits. - Robert Israel, Dec 28 2023

Examples

			Adding the digits of 10 gives 1, a single-digit number, so 10 is a member. Adding the digits of 39 gives 12, which is a 2-digit number, so 39 is not a member. - _Michael B. Porter_, May 16 2018
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Additive Persistence.

Crossrefs

Cf. A000581, A031286.

Cf. Numbers with additive persistence k: A304367 (k=2), A304368 (k=3), A304373 (k=4).

Programs

Maple

select(t -> convert(convert(t,base,10),`+`) < 10, [$10 .. 200]); # Robert Israel, Dec 28 2023

Mathematica

Select[Range@ 120, Length@ FixedPointList[Total@ IntegerDigits@ # &, #] == 3 &] (* Michael De Vlieger, May 14 2018 *)

PARI

nb(n) = {my(nba = 0); while (n > 9, n = sumdigits(n); nba++); nba;}
isok(n) = nb(n) == 1; \\ Michel Marcus, May 13 2018

Formula

A031286(a(n)) = 1.