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%I #10 Jan 08 2021 22:03:54
%S 2,3,7,5,11,23,13,29,37,17,89,47,97,73,19,233,199,157,191,31,41,1597,
%T 521,1741,809,131,107,71,28657,2207,11933,421493,1453,173,487,79,
%U 514229,3571,50549,1103483,2351,733,2063,877,149,433494437,9349,214129,1785473
%N Array read by antidiagonals: row n consists of the primes in row n of the array A333028.
%C 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.
%e Northwest corner:
%e 2 3 5 13 89 233
%e 7 11 29 47 199 521
%e 23 37 97 157 1741 11933
%e 17 73 191 809 421493 1103483
%e 19 31 131 1453 2351 42187
%e 41 107 173 733 55717 236021
%e Row 22 begins with 30631, 2187696161008162875319987.
%t W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 200}];
%t u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k];
%t p[n_] := Table[v[n, k], {k, 1, 1000}];
%t TableForm[Table[Select[p[n], PrimeQ], {n, 1, 100}]]
%Y Cf. A000040, A333028, A333087.
%K nonn,tabl,hard
%O 1,1
%A _Clark Kimberling_, Mar 10 2020
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