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Composite numbers ending in 9.
2

%I #19 Sep 04 2018 09:50:10

%S 9,39,49,69,99,119,129,159,169,189,209,219,249,259,279,289,299,309,

%T 319,329,339,369,399,429,459,469,489,519,529,539,549,559,579,589,609,

%U 629,639,649,669,679,689,699,729,749,759,779,789,799,819,849,869,879,889,899

%N Composite numbers ending in 9.

%C Numbers of the form 10n + 9 (A017377) not in A030433. Obviously multiples of 2 or 5 can't be in A017377 nor this sequence. All other primes occur as factors of these terms infinitely often. For example: If n is a multiple of 3, then 10n + 9 is in this sequence; if n = 4 mod 7, then 10n + 9 is in this sequence; if n = 9 mod 11, then 10n + 9 is in this sequence; and so on and so forth. The first of these congruences to be satisfied determines the least prime factor of 10n + 9. - _Alonso del Arte_, Jun 23 2011

%H G. C. Greubel, <a href="/A053181/b053181.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ 10n. - _Charles R Greathouse IV_, Jun 24 2011

%t Complement[Range[9, 1000, 10], Prime[Range[PrimePi[1000]]]] (* _Alonso del Arte_, Jun 23 2011 *)

%t Select[Range[1000],CompositeQ[#]&&Mod[#,10]==9&] (* _Harvey P. Dale_, May 01 2016 *)

%o (PARI) forstep(n=9,1e3,10,if(!isprime(n),print1(n", "))) \\ _Charles R Greathouse IV_, Jun 24 2011

%K easy,nonn,base

%O 1,1

%A _Enoch Haga_, Feb 29 2000

%E 9 added by _Kausthub Gudipati_, Jun 16 2011