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A228020 Composite numbers whose initial, all intermediate and final iterated digit sums are composite numbers.

%I A228020 #22 Mar 25 2016 16:56:50
%S A228020 4,6,8,9,15,18,22,24,26,27,33,35,36,40,42,44,45,51,54,60,62,63,69,72,
%T A228020 78,80,81,87,90,96,99,105,108,112,114,116,117,121,123,125,126,130,132,
%U A228020 134,135,141,143,144,150,152,153,159,161,162,168,170,171,177,180,186,189,195,198,202,204,206
%N A228020 Composite numbers whose initial, all intermediate and final iterated digit sums are composite numbers.
%C A228020 a(n) is congruent to 0, 4, 6 or 8 mod 9. - _Robert Israel_, Aug 12 2014
%H A228020 Derek Orr, <a href="/A228020/b228020.txt">Table of n, a(n) for n = 1..10000</a>
%e A228020 78 is a term because 78, 7+8 = 15, and 1+5 = 6 are composite.
%p A228020 filter:= proc(n) local x;
%p A228020 x:= n;
%p A228020 do
%p A228020    if isprime(x) then return false fi;
%p A228020    if x < 10 then return (x > 1) fi;
%p A228020    x:= convert(convert(x,base,10),`+`);
%p A228020 od:
%p A228020 end proc;
%p A228020 select(filter,[$4..1000]); # _Robert Israel_, Aug 12 2014
%t A228020 okQ[n_] := n > 1 && !PrimeQ[n] && (n < 10 || okQ@ Total@ IntegerDigits@ n); Select[Range@168, okQ] (* _Giovanni Resta_, Aug 05 2013 *)
%t A228020 cnQ[n_]:=AllTrue[NestWhileList[Total[IntegerDigits[#]]&,n,#>9&], CompositeQ]; Select[Range[210],cnQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 25 2016 *)
%o A228020 (PARI)
%o A228020 forcomposite(n=1,500,s=sumdigits(n);while(s>9&&!isprime(s)&&s!=1,s=sumdigits(s));if(!isprime(s)&&s!=1,print1(n,", "))) \\ _Derek Orr_, Aug 12 2014
%Y A228020 A subset of A228019 and A104211.
%K A228020 nonn,easy,base
%O A228020 1,1
%A A228020 _Derek Orr_, Aug 02 2013