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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
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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Mar 12 2013
STATUS
approved