A281300 Triangular array read by rows: T(n, k) = (((binomial(2*p-1, p-1)-1)/p^3) mod q) + (((binomial(2*q-1, q-1)-1)/q^3) mod p), where p = prime(n) and q = prime(k) for k = 1..n-1.

2, 5, 3, 3, 7, 1, 4, 5, 1, 11, 11, 9, 3, 6, 7, 14, 7, 4, 9, 13, 13, 6, 15, 2, 6, 27, 11, 19, 7, 9, 3, 8, 17, 22, 34, 27, 23, 11, 2, 11, 9, 25, 15, 38, 17, 9, 21, 4, 6, 24, 16, 14, 28, 4, 30, 29, 25, 1, 11, 14, 41, 38, 30, 44, 27, 13, 32, 15, 5, 6, 28, 39, 30

Offset: 1

Author

Felix Fröhlich, Jan 19 2017

Keywords

• nonn
• tabl

Comments

Is p*q always a term of A228562 for T(n, k) = 0?

Is every term t of A228562 a term of A006881 with T(x, y) = 0, where x and y are the indices of the two prime factors of t in A000040?

Examples

			Triangle starts
   2
   5,  3
   3,  7,  1
   4,  5,  1, 11
  11,  9,  3,  6,  7
  14,  7,  4,  9, 13, 13
   6, 15,  2,  6, 27, 11, 19
   7,  9,  3,  8, 17, 22, 34, 27
		

Crossrefs

Cf. A034602, A228562.

Programs

PARI

t(n, k) = my(p=prime(n), q=prime(k)); lift(Mod((binomial(2*q-1, q-1)-1)/q^3, p)) + lift(Mod((binomial(2*p-1, p-1)-1)/p^3, q))
trianglerows(n) = for(x=2, n+1, for(y=1, x-1, print1(t(x, y), ", ")); print(""))
trianglerows(8) \\ print initial 8 rows of triangle

Formula

T(n, k) = A034602(n) % prime(k) + A034602(k) % prime(n).