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
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)
Programs
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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