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A333087
Array (p(n,k)) read by antidiagonals: p(n,k) is the index of the prime in position (n,k) in the array A333086.
2
1, 2, 4, 3, 5, 9, 6, 10, 12, 7, 24, 15, 25, 21, 8, 51, 46, 37, 43, 11, 13, 251, 98, 271, 140, 32, 28, 20, 3121, 329, 1430, 35505, 231, 40, 93, 22, 42613, 500, 5185, 85968, 349, 130, 311, 151, 35
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
Cf. A000040, A099000 (row 1), A333028, A333086.
Sequence in context: A306779 A349947 A351652 * A091451 A365389 A246161
KEYWORD
nonn,tabl,hard
AUTHOR
Clark Kimberling, Mar 10 2020
STATUS
approved