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

1,3

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.

Links

Table of n, a(n) for n=1..57.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000142, A002113, A034886.

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

Sequence in context: A117325 A180643 A017905 * A044962 A044824 A048310

Adjacent sequences: A333595 A333596 A333597 * A333599 A333600 A333601

Keyword

nonn,base

Author

Bernard Schott, Mar 28 2020

Status

approved