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.

0, 13, 37, 71, 157, 263, 457, 599, 1019, 1109, 1607, 1823, 2399, 2647, 2767, 3433, 3697, 4421, 4721, 5501, 6469, 8581, 8951, 9901, 11897, 13577, 14669, 15329, 16229, 16921, 23011, 23531, 23789, 25097, 26153, 32531, 33107, 33997, 34583, 36037, 39079, 43093

Offset

1,2

Comments

The sequence is partly connected with conjecture in A247834. In turn, we conjecture that all terms a(n)>0 for n>1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.
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.

Maple

p:= 1: q:= 2: count:= 0:
while count < 100 do
  if q = p+2 then
    count:= count+1;
    r:= nextprime(floor(p*sqrt(p)));
    if r^2 < p^2*q then A[count]:= r
    else A[count]:= 0 fi;
  fi;
  p:= q; q:= nextprime(p);
od:
seq(A[i], i=1..100); # Robert Israel, Apr 08 2018

Prog

(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

Crossrefs

Cf. A001359, A247834, A247835.

Sequence in context: A233435 A049742 A347209 * A113601 A158864 A003154

Adjacent sequences: A247864 A247865 A247866 * A247868 A247869 A247870

Keyword

nonn

Author

Vladimir Shevelev, Sep 25 2014

Extensions

More terms from Michel Marcus, Sep 25 2014

Status

approved