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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000040, A027748, A246655, A343027.

Sequence in context: A091897 A055201 A213006 * A072303 A242413 A243068

Adjacent sequences: A068995 A068996 A068997 * A068999 A069000 A069001

Keyword

base,easy,nonn

Author

Joseph L. Pe, Mar 16 2002

Extensions

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

Status

approved