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A260458
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Limit of gcd(PP(n) - k, PP(n) + k) as k -> oo, where PP(n) is the product of the first n primes.
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1
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1, 4, 3, 2, 5, 12, 7, 2, 3, 20, 11, 6, 13, 28, 15, 2, 17, 12, 19, 10, 21, 44, 23, 6, 5, 52, 3, 14, 29, 60, 31, 2, 33, 68, 35, 6, 37, 76, 39, 10, 41, 84, 43, 22, 15, 92, 47, 6, 7, 20, 51, 26, 53, 12, 55, 14, 57, 116, 59, 30, 61, 124, 21, 2, 65, 132, 67, 34
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OFFSET
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1,2
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COMMENTS
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a(n) < n if n is in A013929 (numbers that are not squarefree);
a(n) = n if n is in A008578 (primes at beginning of 20th century);
a(n) > n if n is in A039956 (even squarefree numbers).
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LINKS
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EXAMPLE
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For n = 3:
k 2*3*5-k 2*3*5-k GCD
1 29 31 1
2 28 32 4
3 27 33 3
4 26 34 2
For n = 4:
k 2*3*5*7-k 2*3*5*7-k GCD
1 29 31 1
2 28 32 4
3 27 33 3
4 26 34 2
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MATHEMATICA
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z = 120; f[n_] := f[n] = Product[Prime[k], {k, 1, n}];
t[n_, k_] := t[n, k] = GCD[f[n] - k, f[n] + k];
Table[t[50, k], {k, 1, z}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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