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.
FORMULA
a(n) = Prime(1 + PrimePi(n)) - n = A084695(n, 1) (for n > 0). - G. C. Greubel, May 12 2023
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
(SageMath) [next_prime(n) - n for n in range(121)] # G. C. Greubel, May 12 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Incorrect comment removed by Charles R Greathouse IV, Mar 18 2010
More terms from Robert G. Wilson v, Nov 05 2010
STATUS
approved