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

1,2

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Intersection of A002113 and A082939.

Sequence in context: A084399 A067057 A202738 * A286778 A232977 A282819

Adjacent sequences: A082937 A082938 A082939 * A082941 A082942 A082943

Keyword

nonn,base

Author

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

Extensions

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

Status

approved