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Primes that become semiprimes when turned upside down.
1

%I #21 Feb 17 2024 00:46:10

%S 191,691,811,991,1009,1069,1619,1801,1861,1889,6089,6869,6911,6961,

%T 8101,8191,8609,8669,8689,9001,9811,10009,10099,10111,10169,10181,

%U 10601,10889,10891,11119,11161,11689,11699,11801,11969,11981,16061,16691,16699,18089,18119

%N Primes that become semiprimes when turned upside down.

%H Michael S. Branicky, <a href="/A347294/b347294.txt">Table of n, a(n) for n = 1..10000</a>

%H C. K. Caldwell, and G. L. Honaker, Jr., <a href="https://primes.utm.edu/curios/page.php?curio_id=42832">Prime Curio for 191</a>.

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

%t 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 *)

%o (Python)

%o from sympy import isprime, factorint

%o from itertools import count, islice, product

%o def f(s): return s[::-1].translate({ord("6"):ord("9"), ord("9"):ord("6")})

%o def agen():

%o for digits in count(3):

%o for first in "1689":

%o for mid in product("01689", repeat=digits-2):

%o for last in "19":

%o s = first + "".join(mid) + last

%o t = int(s)

%o if isprime(t):

%o flip = f(s)

%o if sum(factorint(int(flip)).values()) == 2:

%o yield t

%o print(list(islice(agen(), 41))) # _Michael S. Branicky_, Feb 16 2024

%Y Cf. A000040, A001358, A048889.

%K nonn,base

%O 1,1

%A _G. L. Honaker, Jr._, Jan 22 2022

%E More terms from _Amiram Eldar_, Jan 23 2022