A084979 Palindromes such that the product of the digits + 1 is prime.

1, 2, 4, 6, 11, 22, 44, 66, 111, 121, 141, 161, 212, 232, 242, 272, 292, 323, 343, 383, 414, 464, 474, 545, 565, 616, 626, 636, 656, 747, 838, 848, 878, 898, 929, 969, 1111, 1221, 1441, 1661, 2112, 2222, 2332, 2552, 2772, 2882, 3223, 3883, 4114, 4444, 4554

Offset: 1

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 21 2003

Keywords

• nonn
• base

Examples

			383 is a term since 3*8*3 = 72, 72+1 = 73 is prime.
		

Links

• J.W.L. (Jan) Eerland, Table of n, a(n) for n = 1..10928

Crossrefs

Cf. A081988.

Programs

Mathematica

Select[ Range[4663], FromDigits[ Reverse[ IntegerDigits[ # ]]] == # && PrimeQ[1 + Times @@ IntegerDigits[ # ]] & ]
Parallelize[While[True,If[PalindromeQ[n]&&PrimeQ[1+Product[Part[IntegerDigits[n],k],{k,1,Length[IntegerDigits[n]]}]],Print[n]];n++];n] (* J.W.L. (Jan) Eerland, Dec 27 2021 *)

Python

from math import prod
from sympy import isprime
from itertools import count, islice, product
def cond(n): return isprime(prod(map(int, str(n))) + 1)
def pals(): # generator of palindromes as strings
    digits = "0123456789"
    for d in count(1):
        for p in product(digits, repeat=d//2):
            if d > 1 and p[0] == "0": continue
            left = "".join(p); right = left[::-1]
            for mid in [[""], digits][d%2]:
                yield int(left + mid + right)
def agen(): yield from filter(cond, pals())
print(list(islice(agen(), 51))) # Michael S. Branicky, Aug 22 2022

Formula

a(n) >> n^k, where k = log_3(10) = 2.0959.... - Charles R Greathouse IV, Aug 02 2010

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jun 21 2003

Formula by Charles R Greathouse IV, Aug 02 2010