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

Author

Patrick De Geest

Keywords

• nonn
• hard
• base
• more

Examples

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

Links

• 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.

Crossrefs

Subsequence of A016115, which is the main entry.

Programs

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

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