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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A309720 A233435 A049742 * 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

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)