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A195325
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Least n-gap prime: a(n) = least prime p for which there is no prime between n*p and n*q, where q is the next prime after p.
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14
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2, 59, 71, 29, 59, 149, 191, 641, 149, 347, 809, 461, 3371, 1487, 857, 1301, 1877, 5849, 4721, 9239, 4271, 1619, 1481, 20507, 20981, 32117, 13337, 19379, 24977, 48779, 20441, 25301, 5651, 37991, 17747, 43577, 176777, 145757, 191249, 84809, 150209, 11717
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OFFSET
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1,1
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COMMENTS
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Such a prime always exists.
The sequence is unbounded.
Conjecture. For n >= 2, a(n) is a lesser of twin primes (A001359). This implies the twin prime conjecture. - Vladimir Shevelev, Sep 15 2011
If a member of this sequence is not the lesser of a twin prime pair, it is greater than 10^10. - Charles R Greathouse IV, Sep 15 2011
A dual sequence: b(n)= least prime p for which there is no prime between n*q and n*p, where q is the previous prime before p. Evidently, b(n) is the next prime after a(n): 3,61,73,31,..., and for n>=2, by the same conjecture, b(n) is a greater of twin primes.
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LINKS
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MAPLE
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a:= proc(n) local p, q;
p:= 2; q:= nextprime(p);
while nextprime(n*p) < (n*q) do
p, q:= q, nextprime(q)
od; p
end:
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MATHEMATICA
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pQ[p_, r_] := Block[{q = NextPrime[p]}, NextPrime[r*p]> r*q]; f[n_] := Block[{p = 2}, While[ !pQ[p, n], p = NextPrime[p]]; p]; f[1] = 2; Array[f, 42] (* Robert G. Wilson v, Sep 18 2011 *) (* Revised by Zak Seidov, Sep 19 2011 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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