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A006567
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Emirps (primes whose reversal is a different prime).
(Formerly M4887)
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143
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13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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REFERENCES
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M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 230.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Glossary, emirp
Eric Weisstein's World of Mathematics, Emirp.
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MAPLE
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read("transforms") ; isA006567 := proc(n) local R ; if isprime(n) then R := digrev(n) ; isprime(R) and R <> n ; else false; end if; end proc:
A006567 := proc(n) option remember ; local a; if n = 1 then 13; else a := nextprime(procname(n-1)) ; while not isA006567(a) do a := nextprime(a) ; end do; return a; end if; end proc:
seq(A006567(n), n=1..120) ; # R. J. Mathar, May 24 2010
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MATHEMATICA
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f[n_] := ToExpression[StringReverse[ToString[n]]]; Select[ Range[ 1200 ], PrimeQ[ f[ # ] ] && PrimeQ[ # ] && f[ # ] != # & ] (* Santi Spadaro, Oct 14 2001 *)
ndig[ a_, b_ ] := 10a + b tonum[ dig_ ] := Fold[ ndig, 0, dig ] f[ n_ ] := tonum[ Reverse[ IntegerDigits[ n ] ] ] Select[ Range[ 1200 ], PrimeQ[ f[ # ] ] && PrimeQ[ # ] && f[ # ] =!= # & ] (* Santi Spadaro, Oct 14 2001 *)
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PROG
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(MAGMA) [ n : n in [1..1194] | n ne rev and IsPrime(n) and IsPrime(rev) where rev is Seqint(Reverse(Intseq(n))) ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) is(n)=my(r=eval(concat(Vecrev(Str(n))))); isprime(r)&&r!=n&&isprime(n) \\ Charles R Greathouse IV, Nov 20 2012
(Haskell)
a006567 n = a006567_list !! (n-1)
a006567_list = filter f a000040_list where
f p = a010051' q == 1 && q /= p where q = a004086 p
-- Reinhard Zumkeller, Jul 16 2014
(Python)
from sympy import prime, isprime
A006567 = [p for p in (prime(n) for n in xrange(1, 10**6)) if str(p) != str(p)[::-1] and isprime(int(str(p)[::-1]))] # Chai Wah Wu, Aug 14 2014
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CROSSREFS
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Cf. A003684, A007628 (subsequence), A046732, A048051, A048052, A048053, A048054, A048895.
A007500 = A002385 union this sequence.
Cf. A000040, A010051, A004086.
Sequence in context: A180526 A161401 A225035 * A246043 A246045 A108388
Adjacent sequences: A006564 A006565 A006566 * A006568 A006569 A006570
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KEYWORD
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nonn,nice,easy,base
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from James A. Sellers, Jan 22 2000
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STATUS
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approved
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