A068998 Numbers m such that the concatenation of the prime factors of m (in increasing order and ignoring multiplicity) is prime.

2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 21, 22, 23, 24, 25, 27, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 46, 47, 48, 49, 51, 53, 54, 58, 59, 61, 63, 64, 66, 67, 70, 71, 72, 73, 79, 81, 82, 83, 88, 89, 92, 93, 96, 97, 99, 101, 103, 107, 108, 109, 111

Offset: 1

Author

Joseph L. Pe, Mar 16 2002

Keywords

• base
• easy
• nonn

Examples

			The prime factors of 51 are 3 and 17 and their concatenation 317 is prime, so 51 belongs to the sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A027748, A246655, A343027.

Programs

Maple

q:= n-> isprime(parse(cat(sort(map(i-> i[1], ifactors(n)[2]))[]))):
select(q, [$2..222])[];  # Alois P. Heinz, Mar 27 2024

Mathematica

Reap[Do[If[PrimeQ[#], Sow[n]] &[FromDigits[Join @@ Map[IntegerDigits, FactorInteger[n][[All, 1]] ] ] ], {n, 120}]][[-1, 1]] (* Michael De Vlieger, Mar 27 2024 *)

Python

def a(n):
    b, s = bin(n)[2:], str(n)
    return int("".join(d for i, d in enumerate(s) if b[i]=="1"))
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Mar 27 2024

Extensions

Missing 4 inserted and more terms from Sean A. Irvine, Mar 27 2024