A046411 - OEIS

%I #28 Jun 12 2021 09:07:19

%S 6,12,18,21,22,28,33,39,46,51,52,54,58,63,66,70,82,84,93,98,111,115,

%T 117,133,141,142,148,154,159,162,165,166,171,172,175,177,182,187,198,

%U 201,205,207,210,219,220,226,232,235,237,245,246,247,249,253,255,261

%N Composite numbers the concatenation of whose prime factors is a prime.

%C For the corresponding primes, see A038514. - _Lekraj Beedassy_, Jun 05 2009

%H Charles R Greathouse IV, <a href="/A046411/b046411.txt">Table of n, a(n) for n = 1..10000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>

%e 162 = 2 * 3 * 3 * 3 * 3 and 23333 is a prime, so 162 is in the sequence.

%t co[n_,k_]:=Nest[FromDigits[Flatten[IntegerDigits[{#,n}]]]&,n,k-1]; Select[Range[261],!PrimeQ[#]&&PrimeQ[FromDigits[Flatten[IntegerDigits[co@@@FactorInteger[#]]]]]&](* _Jayanta Basu_, Jun 04 2013 *)

%o (PARI) is(n)=my(f=factor(n),s="");for(i=1,#f~,for(j=1,f[i,2],s=Str(s,f[i,1]))); isprime(eval(s)) && !isprime(n) \\ _Charles R Greathouse IV_, May 14 2015

%o (Python)

%o from sympy import isprime, factorint

%o def ok(n):

%o     f = factorint(n)

%o     if sum(e for e in f.values()) < 2: return False

%o     return isprime(int("".join(str(p)*e for p, e in f.items())))

%o print(list(filter(ok, range(2, 262)))) # _Michael S. Branicky_, Jun 12 2021

%Y Cf. A037271-A037281.

%Y Cf. A038514 (corresponding primes), A221220 (factors without multiplicity).

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Jun 15 1998

%E Edited by _Charles R Greathouse IV_, Apr 23 2010

%E Title clarified by _Sean A. Irvine_, Jan 16 2021