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

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 20 2003

Keywords

• base
• nonn

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

Examples

			E.g. 12721 is a palindromic prime and 1+2+7+2+1 = 13 is also prime.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002385.

Subsequence of A083393. [Arkadiusz Wesolowski, Sep 14 2011]

Programs

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 *)

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

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