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A006567 Emirps (primes whose reversal is a different prime).
(Formerly M4887)
149
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)
OFFSET

1,1

REFERENCES

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).

LINKS

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.

MAPLE

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

MATHEMATICA

fQ[n_] := Block[{idn = FromDigits@ Reverse@ IntegerDigits@ n}, PrimeQ@ idn && n != idn]; Select[Prime@ Range@ 200, fQ]

(* Santi Spadaro, Oct 14 2001 and modified by Robert G. Wilson v, Nov 08 2015 *)

PROG

(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

CROSSREFS

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 * A263240 A246043 A246045

Adjacent sequences:  A006564 A006565 A006566 * A006568 A006569 A006570

KEYWORD

nonn,nice,easy,base

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Jan 22 2000

STATUS

approved

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Last modified July 27 17:12 EDT 2016. Contains 275099 sequences.