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A333086 Array read by antidiagonals: row n consists of the primes in row n of the array A333028. 2
2, 3, 7, 5, 11, 23, 13, 29, 37, 17, 89, 47, 97, 73, 19, 233, 199, 157, 191, 31, 41, 1597, 521, 1741, 809, 131, 107, 71, 28657, 2207, 11933, 421493, 1453, 173, 487, 79, 514229, 3571, 50549, 1103483, 2351, 733, 2063, 877, 149, 433494437, 9349, 214129, 1785473 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The array shows, in order, the primes in the Wythoff array after deletion of all nonprimes. Every prime occurs exactly once; that is, every prime is uniquely expressible as F(k+1)*floor(n*tau) + (n-1)F(k), where tau = golden ratio (A001622), F = A000045 (Fibonacci numbers), and n and k are positive integers. We assume as true the conjecture that each row is infinite.
LINKS
EXAMPLE
Northwest corner:
2 3 5 13 89 233
7 11 29 47 199 521
23 37 97 157 1741 11933
17 73 191 809 421493 1103483
19 31 131 1453 2351 42187
41 107 173 733 55717 236021
Row 22 begins with 30631, 2187696161008162875319987.
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, 200}];
u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
p[n_] := Table[v[n, k], {k, 1, 1000}];
TableForm[Table[Select[p[n], PrimeQ], {n, 1, 100}]]
CROSSREFS
Sequence in context: A221858 A139317 A117928 * A359504 A064011 A050367
KEYWORD
nonn,tabl,hard
AUTHOR
Clark Kimberling, Mar 10 2020
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)