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URL: https://oeis.org/A228020

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A228020
Composite numbers whose initial, all intermediate and final iterated digit sums are composite numbers.
1
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
1,1
COMMENTS
a(n) is congruent to 0, 4, 6 or 8 mod 9. - Robert Israel, Aug 12 2014
EXAMPLE
78 is a term because 78, 7+8 = 15, and 1+5 = 6 are composite.
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 *)
PROG
(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
CROSSREFS
A subset of A228019 and A104211.
Sequence in context: A254755 A275624 A228019 * A163282 A387186 A095404
KEYWORD
nonn,easy,base
AUTHOR
Derek Orr, Aug 02 2013
STATUS
approved