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A057708
Numbers m such that 2^m reversed is prime.
14
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
1,2
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)
EXAMPLE
4 is a term because 2^4 reversed is 61 and prime.
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 *)
PROG
(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
(PARI) isok(m) = isprime(fromdigits(Vecrev(digits(2^m)))) \\ Mohammed Yaseen, Jul 20 2022
CROSSREFS
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).
Sequence in context: A145018 A018910 A022936 * A032686 A074300 A344157
KEYWORD
base,nonn,more
AUTHOR
G. L. Honaker, Jr., Oct 23 2000
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
STATUS
approved