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A046411
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Composite numbers the concatenation of whose prime factors is a prime.
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12
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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162 = 2 * 3 * 3 * 3 * 3 and 23333 is a prime, so 162 is in the sequence.
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MATHEMATICA
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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 *)
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PROG
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(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())))
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CROSSREFS
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Cf. A038514 (corresponding primes), A221220 (factors without multiplicity).
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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