%I #51 Jul 20 2022 15:19:47

%S 1,4,5,7,10,17,24,37,45,55,70,77,107,137,150,271,364,1157,1656,2004,

%T 2126,3033,3489,3645,4336,6597,7279,12690,13840,20108,21693,28888,

%U 84155,102930

%N Numbers m such that 2^m reversed is prime.

%C a(35) > 105000. - _Giovanni Resta_, Feb 22 2013

%C From _Bernard Schott_, Jan 30 2022: (Start)

%C 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.

%C 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)

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

%p 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:

%t Do[ If[ PrimeQ[ FromDigits[ Reverse[ IntegerDigits[2^n]] ]], Print[ n]], {n, 20000}] (* _Robert G. Wilson v_, Jan 29 2005 *)

%t 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 *)

%o (Python)

%o from sympy import isprime

%o k, m, A057708_list = 1, 2, []

%o while k <= 10**3:

%o if isprime(int(str(m)[::-1])):

%o A057708_list.append(k)

%o k += 1

%o m *= 2 # _Chai Wah Wu_, Mar 09 2021

%o (PARI) isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ _Mohammed Yaseen_, Jul 20 2022

%Y Cf. A004094, A341713.

%Y 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).

%K base,nonn,more

%O 1,2

%A _G. L. Honaker, Jr._, Oct 23 2000

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

%E Two more terms from _Robert G. Wilson v_, Jan 29 2001

%E 3 more terms from _Farideh Firoozbakht_, Aug 05 2004

%E a(33)-a(34) from _Giovanni Resta_, Feb 22 2013