cp's OEIS Frontend

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

%I A377848 #31 Jun 02 2025 18:26:16
%S A377848 4,6,8,10,12,14,16,18,22,104,106,108,112,134,136,138,142,154,156,158,
%T A377848 162,184,186,188,192,194,196,198,202,232,252,262,282,292,302,312,316,
%U A377848 318,320,322,324,332,342,356,358,360,362,364,372,376,378,380,382,384,386
%N A377848 Even numbers which are the sum of two palindromic primes.
%H A377848 Robert Israel, <a href="/A377848/b377848.txt">Table of n, a(n) for n = 1..10000</a>
%e A377848 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 A377848 digrev:= proc(n) local L,i;
%p A377848   L:= convert(n,base,10);
%p A377848   add(L[-i]*10^(i-1),i=1..nops(L))
%p A377848 end proc:
%p A377848 F:= proc(d) # d-digit palindromic primes, d>=3 odd
%p A377848  local R,x,rx,i;
%p A377848     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 A377848 end proc:
%p A377848 PP:= [3,5,7,11,op(F(3))]: nPP:= nops(PP):
%p A377848 A:= {4,seq(seq(PP[i] + PP[j],j=1..i),i=1..nPP)}:
%p A377848 sort(convert(A,list)); # _Robert Israel_, Dec 15 2024
%o A377848 (Python)
%o A377848 from sympy import isprime
%o A377848 from itertools import combinations_with_replacement
%o A377848 def is_palindrome(n):
%o A377848     return str(n) == str(n)[::-1]
%o A377848 palPrimes = set(); sums = set([4]) ; # init sum of 2+2
%o A377848 sumLimit = 1500 # this limit will generate sufficient sequence length for OEIS DATA section
%o A377848 # create list of palindrome primes
%o A377848 for n in range(3,sumLimit):
%o A377848     if isprime(n) and is_palindrome(n):
%o A377848         palPrimes.add(n)
%o A377848 # all combos of 2
%o A377848 c1 = combinations_with_replacement(palPrimes,2)
%o A377848 for i,j in c1:
%o A377848     if (i+j) < sumLimit: sums.add(i+j)
%o A377848 print(sorted(sums))
%o A377848 (PARI) ispal(x) = my(d=digits(x)); d == Vecrev(d);
%o A377848 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 A377848 Intersection of A287961 and A005843.
%Y A377848 Cf. A002385, A379138
%K A377848 nonn,base
%O A377848 1,1
%A A377848 _James S. DeArmon_, Nov 09 2024