A222759 Conjectured number of primes p for which binomial(n*p,p) (mod p^3) does not equal n.

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

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: A357071 A292518 A264997 * A357072 A024940 A324827

Adjacent sequences: A222756 A222757 A222758 * A222760 A222761 A222762

Keyword

nonn

Author

T. D. Noe, Mar 12 2013

Status

approved