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
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
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
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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