OFFSET
1,1
COMMENTS
By Dirichlet's theorem on primes in arithmetic progressions, T(n,k) always exists.
T(n,0) = prime(n).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10191 (rows 1 to 68, flattened)
EXAMPLE
T(4,6) = 13 because prime(4) = 7 and 13 is the first prime == 6 (mod 7).
Triangle begins:
2, 3
3, 7, 2
5, 11, 2, 3, 19
7, 29, 2, 3, 11, 5, 13
11, 23, 2, 3, 37, 5, 17, 7, 19, 31, 43
13, 53, 2, 3, 17, 5, 19, 7, 47, 61, 23, 11, 103
17, 103, 2, 3, 89, 5, 23, 7, 59, 43, 61, 11, 29, 13, 31, 83, 67
MAPLE
h:= proc(p) local A, count, q, v;
A:= Array(0..p-1);
q:= 1; count:= 0;
while count < p do
q:= nextprime(q);
v:= q mod p;
if A[v] = 0 then count:= count+1; A[v]:= q; fi
od;
op(convert(A, list));
end proc:
for i from 1 to 20 do h(ithprime(i)) od;
CROSSREFS
KEYWORD
AUTHOR
Robert Israel, Jan 19 2021
STATUS
approved