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%I M0670 N0247
%S 2,3,5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919,
%T 929,10301,10501,10601,11311,11411,12421,12721,12821,13331,13831,
%U 13931,14341,14741,15451,15551,16061,16361,16561,16661,17471,17971,18181
%N Palindromic primes: prime numbers whose decimal expansion is a palindrome.
%C Every palindrome with an even number of digits is divisible by 11, so 11 is the only member of the sequence with an even number of digits. - _David Wasserman_, Sep 09 2004
%C This holds in any number base A006093(n), n>1. - _Lekraj Beedassy_, Mar 07 2005
%C Subsequence of A188650; A188649(a(n)) = a(n); see A033620 for multiplicative closure. [_Reinhard Zumkeller_, Apr 11 2011]
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 228.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Attila Olah, <a href="/A002385/b002385.txt">Table of n, a(n) for n = 1..100197</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath359.htm">On General Palindromic Numbers</a>
%H C. K. Caldwell, "Top Twenty" page, <a href="http://primes.utm.edu/top20/page.php?id=53">Palindrome</a>
%H P. De Geest, <a href="http://www.worldofnumbers.com/palpri.htm">World!Of Palindromic Primes</a>
%H I. Peterson, Math Trek, <a href="http://www.maa.org/mathland/mathtrek_5_10_99.html">Palindromic Primes</a>
%H M. Shafer, <a href="http://www.egr.msu.edu/~shafermi/primes">First 401066 Palprimes</a> [Broken link]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicPrime.html">Palindromic Prime</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Palindromic_prime">Palindromic prime</a>
%H <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%F Intersection of A000040 (primes) and A002113 (palindromes).
%F A010051(a(n)) * A136522(a(n)) = 1. [_Reinhard Zumkeller_, Apr 11 2011]
%p ff := proc(n) local i,j,k,s,aa,nn,bb,flag; s := n; aa := convert(s,string); nn := length(aa); bb := ``; for i from nn by -1 to 1 do bb := cat(bb,substring(aa,i..i)); od; flag := 0; for j from 1 to nn do if substring(aa,j..j)<>substring(bb,j..j) then flag := 1 fi; od; RETURN(flag); end; gg := proc(i) if ff(ithprime(i)) = 0 then RETURN(ithprime(i)) fi end;
%p rev:=proc(n) local nn, nnn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a:=proc(n) if n=rev(n) and isprime(n)=true then n else fi end: seq(a(n),n=1..20000); # rev is a Maple program to revert a number - _Emeric Deutsch_, Mar 25 2007
%t Select[ Prime[ Range[2100] ], IntegerDigits[#] == Reverse[ IntegerDigits[#] ] & ]
%t lst = {}; e = 3; Do[p = n*10^(IntegerLength[n] - 1) + FromDigits@Rest@Reverse@IntegerDigits[n]; If[PrimeQ[p], AppendTo[lst, p]], {n, 10^e - 1}]; Insert[lst, 11, 5] (* Arkadiusz Wesolowski, May 04 2012 *)
%o (Haskell)
%o a002385 n = a002385_list !! (n-1)
%o a002385_list = filter ((== 1) . a136522) a000040_list
%o -- _Reinhard Zumkeller_, Apr 11 2011
%o (PARI) is(n)=n==eval(concat(Vecrev(Str(n))))&&isprime(n) \\ _Charles R Greathouse IV_, Nov 20 2012
%Y A007500 = this sequence union A006567.
%Y Cf. A016041, A029732, A117697.
%K nonn,base,nice,easy
%O 1,1
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from Larry Reeves (larryr(AT)acm.org), Oct 25 2000
%E Comment from A006093 moved here by _Franklin T. Adams-Watters_, Dec 03 2009
%E Mentioned the sequence A006093 in my comment, previously omitted by mistake _Lekraj Beedassy_, Dec 06 2009
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