A084836 -id:A084836 - cp's OEIS frontend

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

Amarnath Murthy, Jun 23 2001

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

			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.

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

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

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

Corrected and edited by Patrick De Geest, Jun 07 2003

A084837 Palindromic primes with nonincreasing digits up to the middle and then nondecreasing.

Original entry on oeis.org

2, 3, 5, 7, 11, 101, 313, 727, 757, 919, 929, 31013, 72227, 73037, 73237, 74047, 75557, 76367, 76667, 77377, 77477, 91019, 93139, 93239, 94049, 94349, 96269, 96469, 97379, 97579, 98389, 98689, 3211123, 3222223, 3310133, 3321233, 3331333, 7100017, 7300037, 7310137

Offset: 1

Patrick De Geest, Jun 07 2003

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Patrick De Geest, World of Palindromic Primes

Cf. A084836, A062351, A062352.

from sympy import isprime
from itertools import count, islice, combinations_with_replacement as mc
def agen(): # generator of terms
    yield from (2, 3, 5, 7, 11)
    for d in count(2):
        nind = (int("".join(m+m[:-1][::-1])) for m in mc("9876543210", d))
        yield from sorted(filter(isprime, nind))
print(list(islice(agen(), 40))) # Michael S. Branicky, Jun 26 2022

a(38) and beyond from Michael S. Branicky, Jun 26 2022

cp's OEIS Frontend

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

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