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A013632
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Difference between n and the next prime greater than n.
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43
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2, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 2, 1, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 2, 1, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3
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OFFSET
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0,1
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COMMENTS
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Alternatively, a(n) is the smallest positive k such that n + k is prime. - N. J. A. Sloane, Nov 18 2015
Except for a(0) and a(1), a(n) is the least k such that gcd(n!, n + k) = 1. - Robert G. Wilson v, Nov 05 2010
This sequence uses the "strictly larger" variant A151800 of the nextprime function, rather than A007918. Therefore all terms are positive and a(n) = 1 if and only if n + 1 is a prime. - M. F. Hasler, Sep 09 2015
For n > 0, a(n) and n are of opposite parity. Also, by Bertrand's postulate (actually a theorem), for n > 1, a(n) < n. - Zak Seidov, Dec 27 2018
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LINKS
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FORMULA
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EXAMPLE
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a(30) = 1 because 31 is the next prime greater than 30 and 31 - 30 = 1.
a(31) = 6 because 37 is the next prime greater than 31 and 37 - 31 = 6.
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MAPLE
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[ seq(nextprime(i)-i, i=0..100) ];
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MATHEMATICA
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PROG
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(SageMath) [next_prime(n) - n for n in range(121)] # G. C. Greubel, May 12 2023
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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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EXTENSIONS
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STATUS
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approved
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