OFFSET
1,2
COMMENTS
As a sequence, this is a permutation of the positive integers.
EXAMPLE
Northwest corner:
1 2 3 6 24 51
4 5 10 15 46 98
9 12 25 37 271 1430
7 21 43 140 35505 85968
8 11 32 231 349 4410
13 28 40 130 5655 20908
The 4th prime is 7, which occurs in the position (2,1) in A333086, so that p(2,1) = 4.
MATHEMATICA
W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 100}];
u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
p[n_] := Table[v[n, k], {k, 1, 40}];
TableForm[Table[Select[p[n], PrimeQ], {n, 1, 10}]]
t1 = Table[PrimePi[Select[p[n], PrimeQ]], {n, 1, 10}]
tt[n_, k_] := t1[[n]][[k]];
Table[tt[n, k], {n, 1, 10}, {k, 1, 10}] (* A333087 array *)
ttt = Table[tt[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* A333087 sequence *)
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Mar 10 2020
STATUS
approved