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A195325 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. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..169, (first 100 terms from Alois P. Heinz)
MAPLE
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:
seq (a(n), n=1..25); # Alois P. Heinz, Sep 15 2011
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A181866 A106897 A244269 * A195329 A197185 A232848
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 15 2011
STATUS
approved

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Last modified April 18 13:29 EDT 2024. Contains 371780 sequences. (Running on oeis4.)