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A370094
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Rectangular array read by antidiagonals: A(n,k) = prime(A114537(n,k)).
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0
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2, 3, 7, 5, 17, 13, 11, 59, 41, 19, 31, 277, 179, 67, 23, 127, 1787, 1063, 331, 83, 29, 709, 15299, 8527, 2221, 431, 109, 37, 5381, 167449, 87803, 19577, 3001, 599, 157, 43, 52711, 2269733, 1128889, 219613, 27457, 4397, 919, 191, 47, 648391, 37139213
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OFFSET
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1,1
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COMMENTS
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The rows and columns are all increasing, and every prime occurs exactly once.
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LINKS
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FORMULA
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Let f(n) = A007821(n) and p(n) = prime(n). Row n of the array begins with f(n), followed by p(f(n), p(p(f(n))), p(p(p(f(n)))), ...
Also, removing column 1 of array A114537 leaves the present array.
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EXAMPLE
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Corner:
2 3 5 11 31 127 709
7 17 59 277 1787 15299 167449
13 41 179 1063 8527 87803 1128889
19 67 331 2221 19577 219613 3042161
23 83 431 3001 27457 318211 4535189
29 109 599 4397 42043 506683 7474967
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MATHEMATICA
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NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n];
t[n_, k_] := Nest[Prime, NonPrime[n], k];
Table[Prime[t[n - k, k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten
Table[Prime[t[n, k]], {n, 0, 6}, {k, 0, 10}] // TableForm
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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