

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

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Brăduţ Apostol, Laurenţiu Panaitopol, Lucian Petrescu, and László Tóth, Some properties of a sequence defined with the aid of prime numbers, arXiv:1503.01086 [math.NT], 2015.
Brăduţ Apostol, Laurenţiu Panaitopol, Lucian Petrescu, and László Tóth, Some Properties of a Sequence Defined with the Aid of Prime Numbers, J. Int. Seq. 18 (2015) # 15.5.5.


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

Array[NextPrime[#]  # &, 105, 0] (* Robert G. Wilson v, Nov 05 2010 *)


PROG

(PARI) a(n) = nextprime(n+1)  n; \\ Michel Marcus, Mar 04 2015
(Magma) [NextPrime(n)  n: n in [0..100]]; // Vincenzo Librandi, Dec 27 2018


CROSSREFS

Cf. A007918, A151800, A007920.
Sequence in context: A049843 A131374 A207409 * A080121 A122901 A001917
Adjacent sequences: A013629 A013630 A013631 * A013633 A013634 A013635


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

Incorrect comment removed by Charles R Greathouse IV, Mar 18 2010
More terms from Robert G. Wilson v, Nov 05 2010


STATUS

approved



