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A006567 Emirps (primes whose reversal is a different prime).
(Formerly M4887)
143
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

# Contribution from R. J. Mathar, May 24 2010: (Start)

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) ; # (End)

MATHEMATICA

f[n_] := ToExpression[StringReverse[ToString[n]]]; Select[ Range[ 1200 ], PrimeQ[ f[ # ] ] && PrimeQ[ # ] && f[ # ] != # & ] (* from 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[ # ] =!= # & ] (* from Santi Spadaro, Oct 14 2001 *)

PROG

(MAGMA) [ n : n in [1..1194] | n ne rev and IsPrime(n) and IsPrime(rev) where rev is Seqint(Reverse(Intseq(n))) ]; // from 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

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 * A108388 A083983 A129338

Adjacent sequences:  A006564 A006565 A006566 * A006568 A006569 A006570

KEYWORD

nonn,nice,easy,base,changed

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Jan 22 2000

STATUS

approved

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Last modified July 29 09:08 EDT 2014. Contains 245020 sequences.