A350441 Numbers m such that 4^m reversed is prime.

2, 5, 12, 35, 75, 182, 828, 1002, 1063, 2168, 6345, 6920, 10054, 14444, 51465

Offset: 1

Author

Mohammed Yaseen, Dec 31 2021

Keywords

• nonn
• base
• more

Comments

From Bernard Schott, Jan 30 2022: (Start)

If m is a term, then u = 2*m is a term of A057708, because 4^m = 2^(2*m). In fact, terms of this sequence here are half the even terms of A057708.

If m is a term that is multiple of 3, then k = 2*m/3 is a term of A350442, because 4^m = 8^(2m/3). First examples: m = 12, 75, 828, 1002, 6345, 51465, ... and corresponding k = 8, 50, 552, 668, 4230, 34310, ... (End)

Crossrefs

Cf. A058996, A071582.

Cf. Numbers m such that k^m reversed is prime: A057708 (k=2), this sequence (k=4), A058993 (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Programs

Mathematica

Select[Range[2200], PrimeQ[IntegerReverse[4^#]] &] (* Amiram Eldar, Dec 31 2021 *)

PARI

isok(m) = isprime(fromdigits(Vecrev(digits(4^m))))

Python

from sympy import isprime
m = 4
for n in range (1, 2000):
    if isprime(int(str(m)[::-1])):
        print(n)
    m *= 4

Extensions

a(11)-a(15) from Amiram Eldar, Dec 31 2021