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 A006567 Emirps (primes whose reversal is a different prime). (Formerly M4887) 194
 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, 1201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A palindrome is a word that when written in reverse results in the same word. for example, "racecar" reversed is still "racecar". Related to palindromes are semordnilaps. These are words that when written in reverse result in a distinct valid word. For example, "stressed" written in reverse is "desserts". Not all words are palindromes or semordnilaps. While certainly not all numbers are palindromes, all non-palindromic numbers when written in reverse will form semordnilaps. Narrowing to primes brings back the same trichotomy as with words: some numbers are emirps, some numbers are palindromic primes, but some words are neither. The term "emirp" was coined by the American mathematician Jeremiah Farrell (b. 1937). - Amiram Eldar, Jun 11 2021 REFERENCES Martin 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 Chris K. Caldwell, The Prime Glossary, emirp. Brady Haran and N. J. A. Sloane, What Number Comes Next?, Numberphile video, 2018. Eric Weisstein's World of Mathematics, Emirp. Wikipedia, 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 = IntegerReverse@ 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 *) Select[Prime[Range[5, 200]], PrimeQ[IntegerReverse[#]]&&!PalindromeQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2021 *) 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 (PARI) select( {is_A006567(n, r=fromdigits(Vecrev(digits(n))))=isprime(r)&&r!=n&&isprime(n)}, primes(200)) \\ M. F. Hasler, Jan 31 2020 (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 range(1, 10**6)) if str(p) != str(p)[::-1] and isprime(int(str(p)[::-1]))] # Chai Wah Wu, Aug 14 2014 (Python) from sympy import isprime, nextprime def emirps(start=1, end=float('inf')): # generator for emirps in start..end p = nextprime(start-1) while p <= end: s = str(p) if s in "24568": p = nextprime((int(s)+1)*10**(len(s)-1)); continue revp = int(s[::-1]) if p != revp and isprime(revp): yield p p = nextprime(p) print(list(emirps(end=1201))) # Michael S. Branicky, Jan 24 2021, updated Jul 28 2022 CROSSREFS Cf. A003684, A007628 (subsequence), A046732, A048051, A048052, A048053, A048054, A048895, A004086 (read n backwards). A007500 is the union of A002385 and this sequence. Sequence in context: A161401 A225035 A344626 * 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 September 24 17:02 EDT 2023. Contains 365579 sequences. (Running on oeis4.)