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A247867
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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.
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4
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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
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OFFSET
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1,2
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COMMENTS
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The sequence is partly connected with conjecture in A247834. In turn, we conjecture that all terms a(n)>0 for n>1.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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