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

4, 6, 8, 9, 15, 18, 22, 24, 26, 27, 33, 35, 36, 40, 42, 44, 45, 51, 54, 60, 62, 63, 69, 72, 78, 80, 81, 87, 90, 96, 99, 105, 108, 112, 114, 116, 117, 121, 123, 125, 126, 130, 132, 134, 135, 141, 143, 144, 150, 152, 153, 159, 161, 162, 168, 170, 171, 177, 180, 186, 189, 195, 198, 202, 204, 206

Offset: 1

Author

Derek Orr, Aug 02 2013

Keywords

• nonn
• easy
• base

Comments

a(n) is congruent to 0, 4, 6 or 8 mod 9. - Robert Israel, Aug 12 2014

Examples

			78 is a term because 78, 7+8 = 15, and 1+5 = 6 are composite.
		

Links

• Derek Orr, Table of n, a(n) for n = 1..10000

Crossrefs

A subset of A228019 and A104211.

Programs

Maple

filter:= proc(n) local x;
x:= n;
do
   if isprime(x) then return false fi;
   if x < 10 then return (x > 1) fi;
   x:= convert(convert(x,base,10),`+`);
od:
end proc;
select(filter,[$4..1000]); # Robert Israel, Aug 12 2014

Mathematica

okQ[n_] := n > 1 && !PrimeQ[n] && (n < 10 || okQ@ Total@ IntegerDigits@ n); Select[Range@168, okQ] (* Giovanni Resta, Aug 05 2013 *)
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 *)

PARI

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