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A218015 Number of primes p such that sqrt(q) - sqrt(p) > 1/n, where q is the prime after p. 3
0, 6, 22, 41, 75, 132, 186, 258, 330, 416, 511, 613, 724, 860, 1001, 1163, 1372, 1563, 1751, 1965, 2179, 2412, 2685, 2945, 3258, 3581, 3885, 4194, 4525, 4857, 5246, 5644, 6024, 6402, 6767, 7229, 7695, 8177, 8666, 9156, 9674, 10185, 10740, 11283, 11824 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, the number of terms by Andrica ranking which are greater than 1/n.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..200

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

EXAMPLE

a(1) = 6 because only the primes 3, 7, 13, 23, 31 and 113 satisfy the criterion.

As an example, - sqrt(3) + sqrt(5) ~= 0.50401717 which is greater than 1/2.

MATHEMATICA

lst = {}; p = 2; q = 3; While[p < 10^8, If[ Sqrt[q] - Sqrt[p] > 1/50, AppendTo[lst, {p, Sqrt[q] - Sqrt[p]}]]; p = q; q = NextPrime[q]]; Table[ Length@ Select[ lst, #[[2]] > 1/n &], {n, 50}]

nn = 50; t = Table[0, {nn}]; p = 2; q = 3; While[p < 10^8, n = Floor[1/(Sqrt[q] - Sqrt[p])]; If[n <= nn, t[[n]]++]; p = q; q = NextPrime[q]]; Join[{0}, Accumulate[t]] (* T. D. Noe, Oct 18 2012 *)

CROSSREFS

Cf. A079296, A218012, A218014.

Sequence in context: A264043 A056821 A031083 * A031305 A015721 A182200

Adjacent sequences:  A218012 A218013 A218014 * A218016 A218017 A218018

KEYWORD

nonn

AUTHOR

Marek Wolf and Robert G. Wilson v, Oct 18 2012

STATUS

approved

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Last modified April 22 06:14 EDT 2019. Contains 322329 sequences. (Running on oeis4.)