A075517 Created by removing all integers which take an odd number of nested digit sums to reach <10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 28, 29, 37, 38, 39, 46, 47, 48, 49, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 118, 119, 127, 128, 129, 136, 137, 138, 139, 145, 146, 147

Offset: 0

Author

Jon Perry, Oct 11 2002

Keywords

• nonn
• base

Examples

			18 -> 1+8 = 9. This takes 1 step to be reduced to a single integer, hence is not in the sequence. 99 -> 9+9 = 18, takes 2 steps and so is in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007953, A075311.

Programs

Haskell

a075517 n = a075517_list !! n
a075517_list = [0..9] ++ f 1 [0..9] where
   f x ys = if a007953 x `elem` ys then f (x + 1) ys
                                   else x : f (x + 1) (x : ys)
-- Reinhard Zumkeller, Sep 29 2014, Apr 22 2012

Mathematica

ondQ[n_]:=OddQ[Length[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&]]]; Select[Range[0,200],ondQ] (* Harvey P. Dale, Dec 22 2016 *)

PARI

sumdigits(n)=local(c); c=0; while (n>0,c=c+n%10; n=n-n%10; n=n/10); c checkSieve(n)=local(c); c=0; while(n>9, n=sumdigits(n); c++); 1-c%2 for (n=1,2000,if (checkSieve(n),print1(n,",")))

Extensions

Offset fixed by Reinhard Zumkeller, Apr 22 2012

Added a(0) = 0. - Jon Perry, Nov 28 2012