The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A317872 a(n) is the number of times that binomial(n+m, m) mod m = 1, for 0 < m <= n. 1
0, 0, 0, 1, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 2, 2, 1, 1, 3, 2, 0, 0, 1, 2, 2, 4, 4, 4, 0, 0, 3, 4, 1, 1, 3, 3, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 2, 4, 2, 2, 4, 4, 6, 4, 3, 2, 2, 2, 1, 1, 0, 1, 7, 6, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 3, 7, 4, 4, 4, 4, 0, 1, 2, 2, 2, 2, 2, 1, 0, 0, 3, 3, 3, 4, 5, 5, 2, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
COMMENTS
Inspired by A133906.
First occurrence of k with k = 0, 1, 2,...: 1, 4, 10, 9, 27, 100, 54, 64, 176, 544, 352, 648, 649, 129, 128, 1378, 513, 729, 7776, 1377, 5832, 1701, 3728, 13312, 13825, ...
Records: 0, 1, 3, 4, 6, 7, 14, 16, 17, 19, 21, 22, ..., ; and they occur at: 1, 4, 9, 27, 54, 64, 128, 513, 729, 1377, 1701, 3728, 6656, ...
LINKS
EXAMPLE
a(9) = 3 because binomial(9+2,2) mod 2 = binomial(9+3,3) mod 3 = binomial(9+6,6) mod 6 = 1. [Corrected by Jon E. Schoenfield, Aug 28 2018]
MATHEMATICA
a[n_] := Block[{c = 0, m = 1}, While[m < n + 1, If[ Mod[ Binomial[n + m, m], m] == 1, c++]; m++]; c]; Array[a, 105]
Table[Count[Table[Mod[Binomial[n+m, m], m], {m, n}], 1], {n, 120}] (* Harvey P. Dale, Aug 18 2022 *)
CROSSREFS
Cf. A133906.
Sequence in context: A143378 A131961 A276426 * A049340 A336929 A325524
KEYWORD
nonn
AUTHOR
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 10:39 EDT 2024. Contains 373479 sequences. (Running on oeis4.)