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A103160
a(n) = GCD(reverse(n!), reverse((n+1)!)).
0
1, 2, 6, 21, 3, 27, 9, 9, 88263, 9, 99, 594, 198, 99, 99, 99, 99, 99, 99, 9009, 99, 99, 198, 99, 99, 297, 1089, 99, 198, 198, 594, 198, 396, 693, 99, 99, 99, 297, 594, 99, 99, 99, 198, 99, 99, 99, 99, 99, 99, 99, 99, 396, 2772, 99, 99, 99, 396, 693, 693, 99, 99, 99, 99
OFFSET
1,2
COMMENTS
Through the first 200 terms, the largest term has 6 digits with the exception of a(99) which has 134 digits. - Harvey P. Dale, Dec 24 2018
FORMULA
a(n) = GCD(A004153((n+1)!), A004153(n!)).
EXAMPLE
Outstandingly high values arise at n = 10^k - 1 because
A004153(n) = A004153(n+1), a(n) = rev(n!), n! written backwards.
See n = 9, 99, 999, etc.
MATHEMATICA
rd[x_] :=FromDigits[Reverse[IntegerDigits[x]]] Table[GCD[rd[w! ], rd[(w+1)! ]], {w, 1, 100}]
GCD@@#&/@Partition[IntegerReverse[Range[100]!], 2, 1] (* Harvey P. Dale, Dec 24 2018 *)
PROG
(Python)
from math import factorial, gcd
def a(n):
f = factorial(n)
return gcd(int(str(f)[::-1]), int(str(f*(n+1))[::-1]))
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Dec 12 2021
CROSSREFS
Sequence in context: A104861 A074859 A162682 * A242819 A126099 A063753
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Jan 25 2005
STATUS
approved