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A082806 Palindromes which are prime and the sum of the digits is also prime.

%I A082806 #24 Dec 07 2019 12:33:53
%S A082806 2,3,5,7,11,101,131,151,191,313,353,373,757,797,919,10301,10501,11311,
%T A082806 12721,13331,13931,14341,14741,15551,16361,16561,18181,19391,19991,
%U A082806 30103,30703,31513,32323,33533,34543,35153,35353,35753,36563,38183
%N A082806 Palindromes which are prime and the sum of the digits is also prime.
%C A082806 Most of the initial palindromic primes are members.
%C A082806 11 is the only member of even length since the sum of the digits of such palindromes is even and 2 is the only even prime. For the members of odd length the middle digit is odd (except for 2). - _Chai Wah Wu_, Aug 12 2014
%H A082806 Chai Wah Wu, <a href="/A082806/b082806.txt">Table of n, a(n) for n = 1..10000</a>
%e A082806 E.g. 12721 is a palindromic prime and 1+2+7+2+1 = 13 is also prime.
%p A082806 N:= 3: # to get all terms of at most 2*N+1 digits
%p A082806 revdigs:= proc(n)
%p A082806 local L,d;
%p A082806 L:= convert(n,base,10);
%p A082806 d:= nops(L);
%p A082806 add(L[i]*10^(d-i),i=1..d);
%p A082806 end proc:
%p A082806 pals:= proc(d)
%p A082806 local x,y;
%p A082806 seq(seq(x*10^(d+1)+y*10^d + revdigs(x),y=0..9),x=10^(d-1)..10^d-1)
%p A082806 end proc;
%p A082806 select(n -> isprime(n) and isprime(convert(convert(n,base,10),`+`)), {2,3,5,7,11,seq(pals(d),d=1..3)}); # _Robert Israel_, Aug 12 2014
%t A082806 Select[ Range[390000], PrimeQ[ # ] && FromDigits[ Reverse[ IntegerDigits[ # ]]] == # && PrimeQ[ Plus @@ IntegerDigits[ # ]] & ] (* _Robert G. Wilson v_, Jun 17 2003 *)
%o A082806 (Python)
%o A082806 from sympy import isprime
%o A082806 A082806 = sorted([n for n in chain(map(lambda x:int(str(x)+str(x)[::-1]),range(1,10**5)),map(lambda x:int(str(x)+str(x)[-2::-1]), range(1,10**5))) if isprime(n) and isprime(sum([int(d) for d in str(n)]))])
%o A082806 # _Chai Wah Wu_, Aug 12 2014
%Y A082806 Cf. A002385.
%Y A082806 Subsequence of A083393. [_Arkadiusz Wesolowski_, Sep 14 2011]
%K A082806 base,nonn
%O A082806 1,1
%A A082806 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 20 2003
%E A082806 Corrected and extended by _Giovanni Resta_, Feb 07 2006
%E A082806 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 14 2007