OFFSET
1,2
COMMENTS
Equivalently, let S be the set of positive integer multiples of the square roots of the odd primes. Then t(n,k) is the position of k*sqrt(prime(n+1)) in the ordered union of S.
Every positive integer occurs exactly once in the array {t(n,k)}.
EXAMPLE
Northwest corner:
1 5 11 21 31 43 55
2 9 19 34 50 70 91
3 12 26 45 67 93 122
4 18 39 68 101 138 181
6 22 48 79 117 164 211
The numbers 3*k^2 are (3,12,27,48,75,...);
the numbers 5*k^2 are (5,20,45,80,125,...);
the numbers 7*k^2 are (7,28,63,112,175,...);
the joint ranking of all such numbers is (3,5,7,11,12,13,...) = A249370,
in which numbers of the form 3*k^2 occupy positions 1,5,11,21,... which is row 1 of the present array. Similarly, the numbers 5*k^2 occupy positions 2,9,19,34,...
MATHEMATICA
z = 20000; e[h_] := e[h] = Select[Range[2000], Prime[h]*(#^2) < z &];
t = Table[Prime[n]*e[n]^2, {n, 2, 2000}]; s = Sort[Flatten[t]];
u[n_, k_] := Position[s, Prime[n]*k^2];
TableForm[Table[u[n, k], {n, 2, 15}, {k, 1, 15}]] (* A249369 array *)
Table[u[k, n - k + 1], {n, 15}, {k, 1, n}] // Flatten (* A249369 sequence *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 26 2014
STATUS
approved