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A362779
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Triangular array read by rows: T(n,k) is the greatest prime factor of n!*k + 1, n >= 1, 1 <= k <= n.
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2
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2, 3, 5, 7, 13, 19, 5, 7, 73, 97, 11, 241, 19, 37, 601, 103, 131, 2161, 67, 277, 149, 71, 593, 15121, 20161, 79, 30241, 35281, 661, 7331, 1657, 161281, 449, 241921, 282241, 6863, 269, 2477, 1088641, 1451521, 78887, 2177281, 5281, 2903041, 192113, 329891, 29383, 10886401, 62297, 18144001, 2243, 251501, 29030401, 32659201, 843907
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OFFSET
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1,1
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COMMENTS
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The primes in each row are distinct because n!*k + 1 are coprime for 1 <= k <= n, and hence this array gives a simple proof that there are infinitely many prime numbers.
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LINKS
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FORMULA
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EXAMPLE
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Triangle T(n,k) begins:
n\k 1 2 3 4 5 6 ...
1 2
2 3 5
3 7 13 19
4 5 7 73 97
5 11 241 19 37 601
6 103 131 2161 67 277 149
...
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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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