A377848 - OEIS

%I #28 Dec 16 2024 02:13:21

%S 4,6,8,10,12,14,16,18,22,104,106,108,112,134,136,138,142,154,156,158,

%T 162,184,186,188,192,194,196,198,202,232,252,262,282,292,302,312,316,

%U 318,320,322,324,332,342,356,358,360,362,364,372,376,378,380,382,384,386

%N Even numbers which are the sum of two palindromic primes.

%H Robert Israel, <a href="/A377848/b377848.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

%p digrev:= proc(n) local L,i;

%p   L:= convert(n,base,10);

%p   add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p F:= proc(d) # d-digit palindromic primes, d>=3 odd

%p  local R,x,rx,i;

%p     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]))

%p end proc:

%p PP:= [3,5,7,11,op(F(3))]: nPP:= nops(PP):

%p A:= {4,seq(seq(PP[i] + PP[j],j=1..i),i=1..nPP)}:

%p sort(convert(A,list)); # _Robert Israel_, Dec 15 2024

%o (Python)

%o from sympy import isprime

%o from itertools import combinations_with_replacement

%o def is_palindrome(n):

%o     return str(n) == str(n)[::-1]

%o palPrimes = set(); sums = set([4]) ; # init sum of 2+2

%o sumLimit = 1500 # this limit will generate sufficient sequence length for OEIS DATA section

%o # create list of palindrome primes

%o for n in range(3,sumLimit):

%o     if isprime(n) and is_palindrome(n):

%o         palPrimes.add(n)

%o # all combos of 2

%o c1 = combinations_with_replacement(palPrimes,2)

%o for i,j in c1:

%o     if (i+j) < sumLimit: sums.d(i+j)

%o print(sorted(sums))

%o (PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d);

%o 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

%Y Intersection of A287961 and A005843.

%Y Cf. A002385, A379138

%K nonn,base

%O 1,1

%A _James S. DeArmon_, Nov 09 2024