A057708 Numbers m such that 2^m reversed is prime.

1, 4, 5, 7, 10, 17, 24, 37, 45, 55, 70, 77, 107, 137, 150, 271, 364, 1157, 1656, 2004, 2126, 3033, 3489, 3645, 4336, 6597, 7279, 12690, 13840, 20108, 21693, 28888, 84155, 102930

Offset: 1

Author

G. L. Honaker, Jr., Oct 23 2000

Keywords

• base
• nonn
• more

Comments

a(35) > 105000. - Giovanni Resta, Feb 22 2013

From Bernard Schott, Jan 30 2022: (Start)

If m is an even term, then u = m/2 is a term of A350441, this because 2^m = 4^(m/2). In fact, terms of A350441 are half the even terms of this sequence here.

If m is a term multiple of 3, then k = m/3 is a term of A350442, this because 2^m = 8^(m/3). First examples: m = 24, 45, 150, 1656, ... and corresponding k = 8, 15, 50, 552, ... (End)

a(35) > 200000. - Michael S. Branicky, May 12 2025

Examples

			4 is a term because 2^4 reversed is 61 and prime.
		

Crossrefs

Cf. A004094, A341713.

Numbers m such that k^m reversed is prime: this sequence (k=2), A350441 (k=4), A058993 (k=5), A058994 (k=7), A350442 (k=8), A058995 (k=13).

Programs

Maple

with(numtheory): myarray := []: for n from 1 to 4000 do it1 := convert(2^n, base, 10): it2 := sum(10^(nops(it1)-i)*it1[i], i=1..nops(it1)): if isprime(it2) then printf(`%d,`,n) fi: od:

Mathematica

Do[ If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[2^n]] ]], Print[ n]], {n, 20000}] (* Robert G. Wilson v, Jan 29 2005 *)
Select[Range[4400],PrimeQ[IntegerReverse[2^#]]&] (* Requires Mathematica version 10 or later *) (* The program generates the first 25 terms of the sequence; to generate more, increase the Range constant, but the program will take longer to run. *) (* Harvey P. Dale, Aug 05 2020 *)

PARI

isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ Mohammed Yaseen, Jul 20 2022

Python

from sympy import isprime
k, m, A057708_list = 1, 2,  []
while k <= 10**3:
    if isprime(int(str(m)[::-1])):
        A057708_list.append(k)
    k += 1
    m *= 2 # Chai Wah Wu, Mar 09 2021

Extensions

More terms from Chris Nash (chris_nash(AT)prodigy.net), Oct 25 2000

Two more terms from Robert G. Wilson v, Jan 29 2001

3 more terms from Farideh Firoozbakht, Aug 05 2004

a(33)-a(34) from Giovanni Resta, Feb 22 2013