A062351 Palindromic primes with strictly increasing digits up to the middle and then strictly decreasing.

2, 3, 5, 7, 11, 131, 151, 181, 191, 353, 373, 383, 787, 797, 12421, 12721, 12821, 13831, 13931, 14741, 17971, 34543, 34843, 35753, 1235321, 1245421, 1257521, 1268621, 1278721, 1456541, 1469641, 1489841, 1579751, 1589851, 3479743

Offset: 1

Author

Amarnath Murthy, Jun 23 2001

Keywords

• nonn
• base
• easy
• fini
• full

Comments

The last term of the finite series is a(63) = 123467898764321.

Examples

			13831 belongs to the sequence as it is a palindromic prime in which the digits are increasing up to the middle digit 8 and then decreasing.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..63 (complete sequence)
• Patrick De Geest, World of Palindromic Primes

Crossrefs

Cf. A343524 (strictly increasing palindromes), A062352, A084836.

Programs

Python

from sympy import isprime
from itertools import combinations
def agen():
  for digits in range(1, 19):
    for left in combinations("123456789", (digits+1)//2):
      left = "".join(left)
      yield int(left + (left[:digits//2])[::-1])
print(list(filter(isprime, agen()))) # Michael S. Branicky, Apr 25 2021

Extensions

Corrected and edited by Patrick De Geest, Jun 07 2003