A333598 Numbers m such that m! has a palindromic number of decimal digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 22, 30, 37, 44, 57, 63, 69, 70, 81, 86, 91, 106, 111, 116, 126, 131, 140, 145, 154, 163, 168, 177, 186, 199, 221, 225, 238, 242, 255, 259, 288, 292, 368, 372, 384, 388, 407, 411, 419, 423, 438, 450, 532

Offset: 1

Author

Bernard Schott, Mar 28 2020

Keywords

• nonn
• base

Comments

The corresponding palindromic numbers are 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 77, 88, 99, 101, ...

Nice result: 22 is a palindrome and 22! has 22 digits, and also, 44! has 55 digits.

Examples

			14! = 87178291200 that has 11 digits, 11 is a palindrome, hence 14 is a term.
		

Crossrefs

Cf. A000142, A002113, A034886.

Cf. A006488 (similar, with square), A035065 (similar, with prime), A056851 (similar, with cube), A333431 (similar, with factorial).

Programs

Mathematica

Select[Range[0, 532], PalindromeQ @ Length @ IntegerDigits[#!] &] (* Amiram Eldar, Mar 28 2020 *)
Select[Range[0,550],PalindromeQ[IntegerLength[#!]]&] (* Harvey P. Dale, Oct 30 2023 *)

PARI

isok(m) = my(d=digits(#Str(m!))); d == Vecrev(d); \\ Michel Marcus, Mar 28 2020