A377848 Even numbers which are the sum of two palindromic primes.

4, 6, 8, 10, 12, 14, 16, 18, 22, 104, 106, 108, 112, 134, 136, 138, 142, 154, 156, 158, 162, 184, 186, 188, 192, 194, 196, 198, 202, 232, 252, 262, 282, 292, 302, 312, 316, 318, 320, 322, 324, 332, 342, 356, 358, 360, 362, 364, 372, 376, 378, 380, 382, 384, 386

Offset: 1

Author

James S. DeArmon, Nov 09 2024

Keywords

• nonn
• base

Examples

			The first term is 4 (2+2), the second term is 6 (3+3). The first term involving a double-digit addend is 14 (3+11).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A287961 and A005843.

Cf. A002385, A379138

Programs

Maple

digrev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
F:= proc(d) # d-digit palindromic primes, d>=3 odd
 local R,x,rx,i;
    select(isprime,map(t -> seq(10^((d+1)/2)*t + i*10^((d-1)/2) + digrev(t),i=0..9), [$(10^((d-3)/2)) .. 10^((d-1)/2)-1]))
end proc:
PP:= [3,5,7,11,op(F(3))]: nPP:= nops(PP):
A:= {4,seq(seq(PP[i] + PP[j],j=1..i),i=1..nPP)}:
sort(convert(A,list)); # Robert Israel, Dec 15 2024

PARI

ispal(x) = my(d=digits(x)); d == Vecrev(d);
isok(k) = if (!(k%2), forprime(p=2, k\2, if (ispal(p) && isprime(k-p) && ispal(k-p), return(1)))); \\ Michel Marcus, Nov 15 2024

Python

from sympy import isprime
from itertools import combinations_with_replacement
def is_palindrome(n):
    return str(n) == str(n)[::-1]
palPrimes = set(); sums = set([4]) ; # init sum of 2+2
sumLimit = 1500 # this limit will generate sufficient sequence length for OEIS DATA section
# create list of palindrome primes
for n in range(3,sumLimit):
    if isprime(n) and is_palindrome(n):
        palPrimes.add(n)
# all combos of 2
c1 = combinations_with_replacement(palPrimes,2)
for i,j in c1:
    if (i+j) < sumLimit: sums.add(i+j)
print(sorted(sums))