A040025 a(n) is the number of prime palindromes with 2n+1 digits.

4, 15, 93, 668, 5172, 42042, 353701, 3036643, 27045226, 239093865, 2158090933, 19742800564, 180815391365

Offset

0,1

Links

Table of n, a(n) for n=0..12.

Shyam Sunder Gupta, Palindromic Primes up to 10^19.

Shyam Sunder Gupta, Palindromic Primes up to 10^21.

Shyam Sunder Gupta, Palindromic Primes up to 10^23.

Shyam Sunder Gupta, Palindromic Primes up to 10^25.

Example

a(1)=15 because Number of prime palindromes with 3 digits is 15. [Shyam Sunder Gupta, Mar 14 2009]

Prog

(PARI) a(n) = {my(nb = 0); forprime(p=10^(2*n), 10^(2*n+1)-1, if (eval(concat(Vecrev(Str(p)))) == p, nb++); ); nb; } \\ Michel Marcus, Jul 24 2015
(Python)
from sympy import isprime
from itertools import product
def candidate_pals(n): # of length 2n + 1
  if n == 0: yield from [2, 3, 5, 7]; return # one-digit primes
  for rightbutend in product("0123456789", repeat=n-1):
    rightbutend = "".join(rightbutend)
    for end in "1379": # multi-digit primes must end in 1, 3, 7, or 9
      left = end + rightbutend[::-1]
      for mid in "0123456789": yield int(left + mid + rightbutend + end)
def a(n): return sum(isprime(p) for p in candidate_pals(n))
print([a(n) for n in range(6)]) # Michael S. Branicky, Apr 15 2021

Crossrefs

Subsequence of A016115, which is the main entry.

Sequence in context: A372730 A332533 A013193 * A366697 A208991 A109365

Adjacent sequences: A040022 A040023 A040024 * A040026 A040027 A040028

Keyword

nonn,hard,base,more

Author

Patrick De Geest

Extensions

a(9) from Shyam Sunder Gupta, Feb 12 2006

a(10) from Shyam Sunder Gupta, Mar 14 2009

a(11) from Shyam Sunder Gupta, Oct 05 2013

a(12) from Shyam Sunder Gupta, Dec 19 2024

Status

approved