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A179328
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a(n) is the smallest prime q > a(n-1) such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator prime(n) (or 0, if such a prime does not exist).
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3
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3, 23, 139, 293, 1129, 2477, 8467, 30593, 81463, 85933, 190409, 404597, 535399, 840353, 1100977, 2127163, 4640599, 6613631, 6958667, 10343761, 24120233, 49269581, 83751121, 101649649, 166726367, 273469741, 310845683, 568951459
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) > 0 for all n.
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LINKS
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MAPLE
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with(numtheory):
a:= proc(n) option remember; local k, p, q, r, pn;
pn:= ithprime(n);
for k from `if`(n=1, 1, pi(a(n-1))) do
p:= ithprime(k);
q:= ithprime(k+1);
r:= ithprime(k+2);
if denom((q-p)/(r-q)) = pn then break fi
od; q
end:
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MATHEMATICA
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a[n_] := a[n] = Module[{k, p, q, r, pn},
pn = Prime[n];
For[k = If[n == 1, 1, PrimePi[a[n - 1]]], True, k++,
p = Prime[k];
q = Prime[k + 1];
r = Prime[k + 2];
If [Denominator[(q - p)/(r - q)] == pn, Break[]]]; q];
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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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