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

1,1

Links

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

Example

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).

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

Prog

(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.d(i+j)
print(sorted(sums))
(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

Crossrefs

Intersection of A287961 and A005843.

Cf. A002385, A379138

Sequence in context: A175246 A353537 A134928 * A279040 A141109 A333197

Adjacent sequences: A377845 A377846 A377847 * A377849 A377851 A377852

Keyword

nonn,base

Author

James S. DeArmon, Nov 09 2024

Status

approved