login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320920 a(n) is the smallest number m such that binomial(m,n) is nonzero and is divisible by n!. 1
1, 4, 9, 33, 28, 165, 54, 1029, 40832, 31752, 28680, 2588680, 2162700, 12996613, 12341252, 4516741125, 500367376, 133207162881, 93770874890, 7043274506259 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is such that a nontrivial n-symmetric permutation of [1..a(n)] might exist.

LINKS

Table of n, a(n) for n=1..20.

Tanya Khovanova, 3-Symmetric Permutations

EXAMPLE

The sequence of binomial coefficients C(n,3) starts as: 0, 0, 1, 4, 10, 20, 35, 56, 84, 120, 165, and so on. The smallest nonzero number divisible by 3! is 84, which is C(9,3). Therefore a(3) = 9.

PROG

(Python)

from sympy import factorial, binomial

def A320920(n):

    w, m = int(factorial(n)), n

    bc = [int(binomial(n-1, i)) % w for i in range(n+1)]

    while True:

        bc[n] = (bc[n-1]+bc[n]) % w

        if bc[n] == 0:

            return m

        for i in range(n-1, 0, -1):

            bc[i] = (bc[i-1]+bc[i]) % w

        m += 1 # Chai Wah Wu, Oct 25 2018

CROSSREFS

Cf. A042948, A316775, A320919.

Sequence in context: A129196 A119574 A006393 * A048757 A173659 A054433

Adjacent sequences:  A320917 A320918 A320919 * A320921 A320922 A320923

KEYWORD

nonn,more

AUTHOR

Tanya Khovanova, Oct 24 2018

EXTENSIONS

a(14)-a(15) from Alois P. Heinz, Oct 24 2018

a(16)-a(17) from Chai Wah Wu, Oct 25 2018

a(18)-a(19) from Giovanni Resta, Oct 26 2018

a(20) from Giovanni Resta, Oct 27 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 02:40 EST 2019. Contains 319365 sequences. (Running on oeis4.)