A200324 a(n) = floor(10*(sqrt(prime(n+1)) - sqrt(prime(n)))).

3, 5, 4, 6, 2, 5, 2, 4, 5, 1, 5, 3, 1, 2, 4, 4, 1, 3, 2, 1, 3, 2, 3, 4, 2, 0, 1, 0, 1, 6, 1, 2, 0, 4, 0, 2, 2, 1, 2, 2, 0, 3, 0, 1, 0, 4, 4, 1, 0, 1, 1, 0, 3, 1, 1, 1, 0, 1, 1, 0, 2, 4, 1, 0, 1, 3, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 0, 2, 0, 1, 0, 1, 1

Offset

1,1

Comments

If Andrica's conjecture is true, a(n) is at most 1 when n gets very large.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Carlos Rivera, Conjecture 8

Eric Weisstein's World of Mathematics, Andrica's Conjecture

Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945 [math.NT], 2010.

Formula

a(n) = floor(10*(sqrt(A000040(n+1)) - sqrt(A000040(n)))).

Example

a(9) = 5 because 10*(sqrt(29) - sqrt(23)) = 5.8933328382....

Maple

A200324:=n->floor(10*(sqrt(ithprime(n+1))-sqrt(ithprime(n)))): seq(A200324(n), n=1..200); # Wesley Ivan Hurt, Jan 19 2017

Mathematica

Table[Floor[10*(Sqrt[Prime[n + 1]] - Sqrt[Prime[n]])], {n, 100}]
Floor[10(Sqrt[Last[#]]-Sqrt[First[#]])]&/@Partition[Prime[Range[90]], 2, 1] (* Harvey P. Dale, Aug 24 2012 *)

Crossrefs

Cf. A000040, A079063, A200474.

Sequence in context: A057759 A205601 A021286 * A063259 A333717 A064425

Adjacent sequences: A200321 A200322 A200323 * A200325 A200326 A200327

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Nov 18 2011

Status

approved