

A281300


Triangular array read by rows: T(n, k) = (((binomial(2*p1, p1)1)/p^3) mod q) + (((binomial(2*q1, q1)1)/q^3) mod p), where p = prime(n) and q = prime(k) for k = 1..n1.


0



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
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OFFSET

1,1


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?


LINKS

Table of n, a(n) for n=1..73.


FORMULA

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


EXAMPLE

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


PROG

(PARI) t(n, k) = my(p=prime(n), q=prime(k)); lift(Mod((binomial(2*q1, q1)1)/q^3, p)) + lift(Mod((binomial(2*p1, p1)1)/p^3, q))
trianglerows(n) = for(x=2, n+1, for(y=1, x1, print1(t(x, y), ", ")); print(""))
trianglerows(8) \\ print initial 8 rows of triangle


CROSSREFS

Cf. A034602, A228562.
Sequence in context: A141637 A185581 A151960 * A115320 A073480 A077057
Adjacent sequences: A281297 A281298 A281299 * A281301 A281302 A281303


KEYWORD

nonn,tabl


AUTHOR

Felix Fröhlich, Jan 19 2017


STATUS

approved



