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A082806
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Palindromes which are prime and the sum of the digits is also prime.
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6
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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E.g. 12721 is a palindromic prime and 1+2+7+2+1 = 13 is also prime.
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MAPLE
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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
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MATHEMATICA
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Select[ Range[390000], PrimeQ[ # ] && FromDigits[ Reverse[ IntegerDigits[ # ]]] == # && PrimeQ[ Plus @@ IntegerDigits[ # ]] & ] (* Robert G. Wilson v, Jun 17 2003 *)
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PROG
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(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)]))])
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 20 2003
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EXTENSIONS
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STATUS
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approved
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