A093888 Largest palindromic divisor of n!.

1, 1, 2, 6, 8, 8, 9, 252, 252, 252, 48384, 48384, 48384, 48384, 525525, 525525, 525525, 595595, 595595, 969969, 969969, 969969, 405909504, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 5273993725, 290826628092, 290826628092, 290826628092

Offset

0,3

Comments

As positive palindromes do not end in 0 terms are not a multiple of 10. - David A. Corneth, Oct 07 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 0..60 (terms 1..40 from David A. Corneth)

David A. Corneth, Lower bounds for a(0)..a(100)

Formula

a(n) = A093030(A000142(n)). - Michel Marcus, Oct 12 2022

Example

a(8) = 252 as 252 is the largest palindrome that divides 8! = 40320.

Mathematica

Table[SelectFirst[Reverse[Divisors[n!]], PalindromeQ], {n, 30}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2020 *)

Prog

(PARI) a(n) = { res = 1; my(d = divisors(n! >> val(n, 2))); forstep(i = #d, 1, -1, if(ispal(d[i]), res = d[i]; break; ) ); d = divisors(n! / 5^val(n, 5)); forstep(i = #d, 1, -1, if(d[i] < res, return(res); ); if(ispal(d[i]), res = d[i]; break; ) ); res }
ispal(n) = my(d = digits(n)); d == Vecrev(d)
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Oct 07 2022
(Python)
from sympy import divisors, factorial, multiplicity
def ispal(n): s = str(n); return s == s[::-1]
def b(n, k): f = factorial(n); return f//k**multiplicity(k, f)
def a(n):
    m2 = max(d for d in divisors(b(n, 2), generator=True) if ispal(d))
    m5 = max(d for d in divisors(b(n, 5), generator=True) if ispal(d))
    return max(m2, m5)
print([a(n) for n in range(34)]) # Michael S. Branicky, Oct 12 2022 after David A. Corneth

Crossrefs

Cf. A000142, A002113, A093030, A093889.

Sequence in context: A236676 A021376 A243311 * A136702 A328910 A064165

Adjacent sequences: A093885 A093886 A093887 * A093889 A093890 A093891

Keyword

base,nonn

Author

Amarnath Murthy, Apr 23 2004

Extensions

More terms from Jason Earls, May 07 2004

a(0) and more terms from David A. Corneth, Oct 07 2022

Status

approved