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 A082806 Palindromes which are prime and the sum of the digits is also prime. 6
 2, 3, 5, 7, 11, 101, 131, 151, 191, 313, 353, 373, 757, 797, 919, 10301, 10501, 11311, 12721, 13331, 13931, 14341, 14741, 15551, 16361, 16561, 18181, 19391, 19991, 30103, 30703, 31513, 32323, 33533, 34543, 35153, 35353, 35753, 36563, 38183 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Most of the initial palindromic primes are members. 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 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE E.g. 12721 is a palindromic prime and 1+2+7+2+1 = 13 is also prime. MAPLE N:= 3: # to get all terms of at most 2*N+1 digits revdigs:= proc(n) local L, d; L:= convert(n, base, 10); d:= nops(L); add(L[i]*10^(d-i), i=1..d); end proc: pals:= proc(d) local x, y; seq(seq(x*10^(d+1)+y*10^d + revdigs(x), y=0..9), x=10^(d-1)..10^d-1) end proc; 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 MATHEMATICA Select[ Range[390000], PrimeQ[ # ] && FromDigits[ Reverse[ IntegerDigits[ # ]]] == # && PrimeQ[ Plus @@ IntegerDigits[ # ]] & ] (* Robert G. Wilson v, Jun 17 2003 *) PROG (Python) from sympy import isprime 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)]))]) # Chai Wah Wu, Aug 12 2014 CROSSREFS Cf. A002385. Subsequence of A083393. [Arkadiusz Wesolowski, Sep 14 2011] Sequence in context: A083139 A088562 A083712 * A157868 A222116 A229107 Adjacent sequences:  A082803 A082804 A082805 * A082807 A082808 A082809 KEYWORD base,nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 20 2003 EXTENSIONS Corrected and extended by Giovanni Resta, Feb 07 2006 Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007 STATUS approved

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Last modified April 11 03:50 EDT 2021. Contains 342886 sequences. (Running on oeis4.)