OFFSET
2,1
COMMENTS
The maximum deck size to perform the n-card trick using the Fitch Cheney method. This trick is known as the 5-card trick, where the maximum deck size is 52.
The method was later improved to serve a bigger deck described by A030495. In particular, the 5-card trick can be performed with the deck of size 124, and this size is the largest possible.
a(n) = A275929(n)-2.
REFERENCES
Wallace Lee, Math Miracles, published by Seeman Printery, Durham, N.C., 1950.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 2..450
Aria Chen, Tyler Cummins, Rishi De Francesco, Jate Greene, Tanya Khovanova, Alexander Meng, Tanish Parida, Anirudh Pulugurtha, Anand Swaroop, and Samuel Tsui, Card Tricks and Information, arXiv:2405.21007 [math.HO], 2024. See p. 9.
FORMULA
E.g.f.: 1 + exp(x)*(x - 1) - 2*(x - log(1 - x)). - Stefano Spezia, Jun 06 2024
MATHEMATICA
Table[(k - 1) (2 Factorial[k - 2] + 1), {k, 2, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova and PRIMES STEP junior group, Mar 05 2024
STATUS
approved