A082940 Palindromes in A082939.

1, 2, 22, 141, 171, 202, 333, 2002, 2772, 7227, 10401, 10701, 12221, 13131, 14841, 15651, 16461, 17271, 20002, 21212, 25452, 26262, 27072, 30303, 31113, 33633, 35253, 41814, 51615, 52425, 53235, 55755, 58185, 61416, 62226, 66366, 69696, 71217, 72027, 85158, 96669, 117711

Offset: 1

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 27 2003, following a suggestion by Amarnath Murthy

Keywords

• nonn
• base

Examples

			22 = 2!*2! = 4 and 2 + 2 = 4.
141 = 1!*4!*1! = 24; 2 + 4 = 6 and 1 + 4 + 1 = 6.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..670 from J.W.L. (Jan) Eerland)

Crossrefs

Intersection of A002113 and A082939.

Programs

Mathematica

DeleteCases[ParallelTable[If[PalindromeQ[n]&&Total@IntegerDigits[Times@@Map[Factorial,IntegerDigits[n]]]==Total@IntegerDigits[n],n,a],{n,0,10^8}],a] (* J.W.L. (Jan) Eerland, Dec 26 2021 *)

Python

from math import factorial, prod
from itertools import count, islice, product
def isA082939(n):
    d = list(map(int, str(n)))
    return sum(map(int, str(prod(map(factorial, d))))) == sum(d)
def pals(): # generator of terms
    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(isA082939, pals())
print(list(islice(agen(), 42))) # Michael S. Branicky, Aug 15 2022

Extensions

Corrected and extended by J.W.L. (Jan) Eerland, Dec 26 2021