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A013632 Difference between n and the next prime greater than n. 31
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 (list; graph; refs; listen; history; text; internal format)
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 the 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

LINKS

Table of n, a(n) for n=0..104.

Brăduţ Apostol, Laurenţiu Panaitopol, Lucian Petrescu, 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, 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

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

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Last modified November 18 11:06 EST 2018. Contains 317302 sequences. (Running on oeis4.)