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

%I A075517 #28 Sep 04 2017 09:22:42
%S A075517 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,
%T A075517 65,66,67,68,69,73,74,75,76,77,78,79,82,83,84,85,86,87,88,89,91,92,93,
%U A075517 94,95,96,97,98,99,109,118,119,127,128,129,136,137,138,139,145,146,147
%N A075517 Created by removing all integers which take an odd number of nested digit sums to reach <10.
%H A075517 Reinhard Zumkeller, <a href="/A075517/b075517.txt">Table of n, a(n) for n = 0..10000</a>
%e A075517 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.
%t A075517 ondQ[n_]:=OddQ[Length[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&]]]; Select[Range[0,200],ondQ] (* _Harvey P. Dale_, Dec 22 2016 *)
%o A075517 (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,",")))
%o A075517 (Haskell)
%o A075517 a075517 n = a075517_list !! n
%o A075517 a075517_list = [0..9] ++ f 1 [0..9] where
%o A075517    f x ys = if a007953 x `elem` ys then f (x + 1) ys
%o A075517                                    else x : f (x + 1) (x : ys)
%o A075517 -- Reinhard Zumkeller, Sep 29 2014, Apr 22 2012
%Y A075517 Cf. A007953, A075311.
%K A075517 nonn,base
%O A075517 0,3
%A A075517 _Jon Perry_, Oct 11 2002
%E A075517 Offset fixed by _Reinhard Zumkeller_, Apr 22 2012
%E A075517 Added a(0) = 0. - _Jon Perry_, Nov 28 2012