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A247867 a(n) is the smallest prime in the interval [k*sqrt(k), k*sqrt(k+2)], where k = A001359(n), or a(n)=0 if there is no prime in this interval.

%I A247867 #23 Apr 09 2018 02:49:05
%S A247867 0,13,37,71,157,263,457,599,1019,1109,1607,1823,2399,2647,2767,3433,
%T A247867 3697,4421,4721,5501,6469,8581,8951,9901,11897,13577,14669,15329,
%U A247867 16229,16921,23011,23531,23789,25097,26153,32531,33107,33997,34583,36037,39079,43093
%N A247867 a(n) is the smallest prime in the interval [k*sqrt(k), k*sqrt(k+2)], where k = A001359(n), or a(n)=0 if there is no prime in this interval.
%C A247867 The sequence is partly connected with conjecture in A247834. In turn, we conjecture that all terms a(n)>0 for n>1.
%H A247867 Robert Israel, <a href="/A247867/b247867.txt">Table of n, a(n) for n = 1..10000</a>
%e A247867 For n=1, k=A001359(1)=3, we have the interval [3*sqrt(3), 3*sqrt(5)] = [5.1...,6.7...] which does not contain a prime. So, a(1)=0.
%e A247867 For n=2, k=5, we have the interval [5*sqrt(5), 5*sqrt(7)] = [11.1..., 13.2...] which contains only one prime: 13. So, a(2)=13.
%p A247867 p:= 1: q:= 2: count:= 0:
%p A247867 while count < 100 do
%p A247867   if q = p+2 then
%p A247867     count:= count+1;
%p A247867     r:= nextprime(floor(p*sqrt(p)));
%p A247867     if r^2 < p^2*q then A[count]:= r
%p A247867     else A[count]:= 0 fi;
%p A247867   fi;
%p A247867   p:= q; q:= nextprime(p);
%p A247867 od:
%p A247867 seq(A[i],i=1..100); # _Robert Israel_, Apr 08 2018
%o A247867 (PARI) lista(nn) = {forprime(p=2, nn, if (isprime(q=p+2), pmin = nextprime(ceil(p*sqrt(p))); if (pmin <= floor(p*sqrt(q)), val = pmin, val = 0); print1(val, ", ");););} \\ _Michel Marcus_, Sep 25 2014
%Y A247867 Cf. A001359, A247834, A247835.
%K A247867 nonn
%O A247867 1,2
%A A247867 _Vladimir Shevelev_, Sep 25 2014
%E A247867 More terms from _Michel Marcus_, Sep 25 2014