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

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

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