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

2, 3, 5, 6, 7, 11, 12, 13, 17, 18, 19, 21, 22, 23, 28, 29, 31, 33, 37, 39, 41, 43, 46, 47, 51, 52, 53, 54, 58, 59, 61, 63, 66, 67, 70, 71, 73, 79, 82, 83, 84, 89, 93, 97, 98, 101, 103, 107, 109, 111, 113, 115, 117, 127, 131, 133, 137, 139, 141, 142, 148, 149

Offset

1,1

Links

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

Example

c(1) = 1    not prime -> 1 is not a term.
c(2) = 2    prime     -> 2 is a term.
c(3) = 3    prime     -> 3 is a term.
c(4) = 22   not prime -> 4 is not a term.
c(5) = 5    prime     -> 5 is a term.
c(6) = 23   prime     -> 6 is a term.

Maple

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

Mathematica

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 *)

Prog

(Python)
from sympy import *
def b(n):
    f=factorint(n)
    l=sorted(f)
    return 1 if n==1 else int("".join(str(i)*f[i] for i in l))
# print([b(n) for n in range(1, 101)])
for n in range(1, 200):
    if isprime(b(n)):
        print (n)

Crossrefs

Cf. A037276 (concatenate prime factors), A046411.

Cf. A068998.

Sequence in context: A367585 A164922 A205523 * A145739 A198191 A243058

Adjacent sequences: A343024 A343025 A343026 * A343028 A343029 A343030

Keyword

nonn,base

Author

Wim JA Bruyninckx, Apr 02 2021

Status

approved