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A200324 Floor(10*(sqrt(prime(n+1))-sqrt(prime(n)))). 2
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 (list; graph; refs; listen; history; text; internal format)
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)

FORMULA

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

EXAMPLE

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

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 A064425 A094761

Adjacent sequences:  A200321 A200322 A200323 * A200325 A200326 A200327

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Nov 18 2011

STATUS

approved

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Last modified November 22 18:51 EST 2014. Contains 249807 sequences.