

A343027


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


1



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
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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.


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: A355647 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



