A347294 Primes that become semiprimes when turned upside down.

191, 691, 811, 991, 1009, 1069, 1619, 1801, 1861, 1889, 6089, 6869, 6911, 6961, 8101, 8191, 8609, 8669, 8689, 9001, 9811, 10009, 10099, 10111, 10169, 10181, 10601, 10889, 10891, 11119, 11161, 11689, 11699, 11801, 11969, 11981, 16061, 16691, 16699, 18089, 18119

Offset

1,1

Links

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

C. K. Caldwell, and G. L. Honaker, Jr., Prime Curio for 191.

Example

811 is a term because when 811 is turned upside down (rotated 180 degrees) it becomes 118=2*59, a semiprime.

Mathematica

semiQ[n_] := PrimeOmega[n] == 2; q[n_] := PrimeQ[n] && Module[{d = IntegerDigits[n]}, AllTrue[d, MemberQ[{0, 1, 6, 8, 9}, #] &] && semiQ[FromDigits[Reverse[d] /. {6 -> 9, 9 -> 6}]]]; Select[Range[20000], q] (* Amiram Eldar, Jan 23 2022 *)

Prog

(Python)
from sympy import isprime, factorint
from itertools import count, islice, product
def f(s): return s[::-1].translate({ord("6"):ord("9"), ord("9"):ord("6")})
def agen():
    for digits in count(3):
        for first in "1689":
            for mid in product("01689", repeat=digits-2):
                for last in "19":
                    s = first + "".join(mid) + last
                    t = int(s)
                    if isprime(t):
                        flip = f(s)
                        if sum(factorint(int(flip)).values()) == 2:
                            yield t
print(list(islice(agen(), 41))) # Michael S. Branicky, Feb 16 2024

Crossrefs

Cf. A000040, A001358, A048889.

Sequence in context: A142562 A142619 A337791 * A086878 A082445 A108848

Adjacent sequences: A347291 A347292 A347293 * A347295 A347296 A347297

Keyword

nonn,base

Author

G. L. Honaker, Jr., Jan 22 2022

Extensions

More terms from Amiram Eldar, Jan 23 2022

Status

approved