

A013632


Difference between n and the next prime greater than n.


43



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

0,1


COMMENTS

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


LINKS



FORMULA



EXAMPLE

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.


MAPLE

[ seq(nextprime(i)i, i=0..100) ];


MATHEMATICA



PROG

(SageMath) [next_prime(n)  n for n in range(121)] # G. C. Greubel, May 12 2023


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



