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A343027 Numbers whose concatenation of prime factors in increasing order is a prime number.

%I A343027 #30 Mar 27 2024 10:58:32
%S A343027 2,3,5,6,7,11,12,13,17,18,19,21,22,23,28,29,31,33,37,39,41,43,46,47,
%T A343027 51,52,53,54,58,59,61,63,66,67,70,71,73,79,82,83,84,89,93,97,98,101,
%U A343027 103,107,109,111,113,115,117,127,131,133,137,139,141,142,148,149
%N A343027 Numbers whose concatenation of prime factors in increasing order is a prime number.
%H A343027 Michael S. Branicky, <a href="/A343027/b343027.txt">Table of n, a(n) for n = 1..10000</a>
%e A343027 c(1) = 1    not prime -> 1 is not a term.
%e A343027 c(2) = 2    prime     -> 2 is a term.
%e A343027 c(3) = 3    prime     -> 3 is a term.
%e A343027 c(4) = 22   not prime -> 4 is not a term.
%e A343027 c(5) = 5    prime     -> 5 is a term.
%e A343027 c(6) = 23   prime     -> 6 is a term.
%p A343027 q:= n-> isprime(parse(cat(sort(map(i-> i[1]$i[2], ifactors(n)[2]))[]))):
%p A343027 select(q, [$2..222])[];  # _Alois P. Heinz_, Mar 27 2024
%t A343027 m[{p_, e_}] := Table[p, {e}]; c[w_] := FromDigits[Join @@ IntegerDigits@ w]; Select[ Range@ 150, PrimeQ@ c@ Flatten[m /@ FactorInteger[#]] &] (* _Giovanni Resta_, Apr 23 2021 *)
%o A343027 (Python)
%o A343027 from sympy import *
%o A343027 def b(n):
%o A343027     f=factorint(n)
%o A343027     l=sorted(f)
%o A343027     return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
%o A343027 # print([b(n) for n in range(1, 101)])
%o A343027 for n in range(1,200):
%o A343027     if isprime(b(n)):
%o A343027         print (n)
%Y A343027 Cf. A037276 (concatenate prime factors), A046411.
%Y A343027 Cf. A068998.
%K A343027 nonn,base
%O A343027 1,1
%A A343027 _Wim JA Bruyninckx_, Apr 02 2021