# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a006567 Showing 1-1 of 1 %I A006567 M4887 #81 Oct 02 2023 02:39:02 %S A006567 13,17,31,37,71,73,79,97,107,113,149,157,167,179,199,311,337,347,359, %T A006567 389,701,709,733,739,743,751,761,769,907,937,941,953,967,971,983,991, %U A006567 1009,1021,1031,1033,1061,1069,1091,1097,1103,1109,1151,1153,1181,1193,1201 %N A006567 Emirps (primes whose reversal is a different prime). %C A006567 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. %C A006567 The term "emirp" was coined by the American mathematician Jeremiah Farrell (1937-2022). - _Amiram Eldar_, Jun 11 2021 %D A006567 Martin Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 230. %D A006567 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A006567 T. D. Noe, Table of n, a(n) for n = 1..10000 %H A006567 Chris K. Caldwell, The Prime Glossary, emirp. %H A006567 Brady Haran and N. J. A. Sloane, What Number Comes Next?, Numberphile video, 2018. %H A006567 Eric Weisstein's World of Mathematics, Emirp. %H A006567 Wikipedia, Emirp. %p A006567 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: %p A006567 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: %p A006567 seq(A006567(n),n=1..120) ; # _R. J. Mathar_, May 24 2010 %t A006567 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 *) %t A006567 Select[Prime[Range[5,200]],PrimeQ[IntegerReverse[#]]&&!PalindromeQ[#]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 11 2021 *) %o A006567 (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 %o A006567 (PARI) is(n)=my(r=eval(concat(Vecrev(Str(n)))));isprime(r)&&r!=n&&isprime(n) \\ _Charles R Greathouse IV_, Nov 20 2012 %o A006567 (PARI) select( {is_A006567(n,r=fromdigits(Vecrev(digits(n))))=isprime(r)&&r!=n&&isprime(n)}, primes(200)) \\ _M. F. Hasler_, Jan 31 2020 %o A006567 (Haskell) %o A006567 a006567 n = a006567_list !! (n-1) %o A006567 a006567_list = filter f a000040_list where %o A006567 f p = a010051' q == 1 && q /= p where q = a004086 p %o A006567 -- _Reinhard Zumkeller_, Jul 16 2014 %o A006567 (Python) %o A006567 from sympy import prime, isprime %o A006567 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 %o A006567 (Python) %o A006567 from sympy import isprime, nextprime %o A006567 def emirps(start=1, end=float('inf')): # generator for emirps in start..end %o A006567 p = nextprime(start-1) %o A006567 while p <= end: %o A006567 s = str(p) %o A006567 if s[0] in "24568": %o A006567 p = nextprime((int(s[0])+1)*10**(len(s)-1)); continue %o A006567 revp = int(s[::-1]) %o A006567 if p != revp and isprime(revp): yield p %o A006567 p = nextprime(p) %o A006567 print(list(emirps(end=1201))) # _Michael S. Branicky_, Jan 24 2021, updated Jul 28 2022 %Y A006567 Cf. A003684, A007628 (subsequence), A046732, A048051, A048052, A048053, A048054, A048895, A004086 (read n backwards). %Y A006567 A007500 is the union of A002385 and this sequence. %K A006567 nonn,nice,easy,base %O A006567 1,1 %A A006567 _N. J. A. Sloane_ %E A006567 More terms from _James A. Sellers_, Jan 22 2000 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE