

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
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OFFSET

1,2


COMMENTS

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


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



