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A343027 Numbers whose concatenation of prime factors in increasing order is a prime number. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..62.

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.

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.

Sequence in context: A129128 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

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Last modified November 29 14:50 EST 2021. Contains 349416 sequences. (Running on oeis4.)