login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A222759 Conjectured number of primes p for which binomial(n*p,p) (mod p^3) does not equal n. 3
0, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It appears that, for k > 2 and n >= prime(prime(k)^3), then a(n) >= k.

Sequences A000720 and A056811 give results for binomial(n*p,p) (mod p) and binomial(n*p,p) (mod p^2), respectively. It appears that mod p^3 is the last case; that is, this identity does not hold for higher powers. - T. D. Noe, Mar 14 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

MATHEMATICA

Table[Length[Select[Prime[Range[100]], Mod[Binomial[n*#, #], #^3] != n &]], {n, 87}]

CROSSREFS

Cf. A096328 (prime(prime(n)^3).

Cf. A000720, A056811 (primePi(n) and primePi(sqrt(n))).

Sequence in context: A240718 A292518 A264997 * A024940 A324827 A205217

Adjacent sequences:  A222756 A222757 A222758 * A222760 A222761 A222762

KEYWORD

nonn

AUTHOR

T. D. Noe, Mar 12 2013

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 April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)