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
Examples
a(9) = 5 because 10*(sqrt(29) - sqrt(23)) = 5.8933328382....
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.
Programs
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Maple
A200324:=n->floor(10*(sqrt(ithprime(n+1))-sqrt(ithprime(n)))): seq(A200324(n), n=1..200); # Wesley Ivan Hurt, Jan 19 2017
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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 *)
Comments