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
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
Programs
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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
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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))