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A080790
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Binary emirps, primes whose binary reversal is a different prime.
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6
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11, 13, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 83, 97, 101, 113, 131, 151, 163, 167, 173, 181, 193, 197, 199, 223, 227, 229, 233, 251, 263, 269, 277, 283, 307, 331, 337, 349, 353, 359, 373, 383, 409, 421, 431, 433, 449, 461, 463, 479, 487, 491, 503, 509, 521
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Members of A074832 that are not in A006995. - Robert Israel, Aug 31 2016
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..10000
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EXAMPLE
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A000040(10)=29 -> '11101' rev '10111' -> 23=A000040(9), therefore 29 and 23 are terms.
The prime 19 is not a term, as 19 -> '10011' rev '11001' -> 25=5^2; and 7=A074832(3) is not a term because it is a binary palindrome (A006995) and therefore not different.
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MAPLE
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revdigs:= proc(n) local L; L:= convert(n, base, 2); add(L[-i]*2^(i-1), i=1..nops(L)) end proc:
filter:= proc(t) local r; if not isprime(t) then return false fi;
r:= revdigs(t); r <> t and isprime(r) end proc:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Aug 30 2016
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PROG
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(Python)
from sympy import isprime
def ok(n):
r = int(bin(n)[2:][::-1], 2)
return n != r and isprime(n) and isprime(r)
print([k for k in range(600) if ok(k)]) # Michael S. Branicky, Jul 30 2022
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CROSSREFS
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Cf. A006567, A006995, A074832, A004676, A007088.
Sequence in context: A075519 A019406 A289688 * A066123 A048393 A136058
Adjacent sequences: A080787 A080788 A080789 * A080791 A080792 A080793
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Mar 25 2003
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STATUS
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approved
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