A046411 Composite numbers the concatenation of whose prime factors is a prime.

6, 12, 18, 21, 22, 28, 33, 39, 46, 51, 52, 54, 58, 63, 66, 70, 82, 84, 93, 98, 111, 115, 117, 133, 141, 142, 148, 154, 159, 162, 165, 166, 171, 172, 175, 177, 182, 187, 198, 201, 205, 207, 210, 219, 220, 226, 232, 235, 237, 245, 246, 247, 249, 253, 255, 261

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Comments

For the corresponding primes, see A038514. - Lekraj Beedassy, Jun 05 2009

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Home Primes

Crossrefs

Cf. A037271-A037281.

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

Programs

Mathematica

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 *)

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

Python

from sympy import isprime, factorint
def ok(n):
    f = factorint(n)
    if sum(e for e in f.values()) < 2: return False
    return isprime(int("".join(str(p)*e for p, e in f.items())))
print(list(filter(ok, range(2, 262)))) # Michael S. Branicky, Jun 12 2021

Extensions

Edited by Charles R Greathouse IV, Apr 23 2010

Title clarified by Sean A. Irvine, Jan 16 2021