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URL: https://oeis.org/A338578

⇱ A338578 - OEIS

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A338578
Primes p such that (r-p)*(r-q) > r, where q and r are the next two primes.
2
2, 3, 5, 11, 17, 19, 29, 43, 47, 83, 109, 199, 283
OFFSET
1,1
COMMENTS
a(14) > 10^8 if it exists.
As soon as the prime gap grows slow enough, for all large enough p we have (r-p)*(r-q) <= r, implying finiteness of this sequence. In particular, finiteness would follow from Cramer's conjecture. - Max Alekseyev, Nov 09 2024
EXAMPLE
a(5)=17 is a member because it is prime, the next two primes are 19 and 23, and (23-17)*(23-19)=24 > 23.
MAPLE
p:= 0: q:=2:r:= 3: R:= NULL:
while p < 10^4 do
p:= q: q:= r: r:= nextprime(r);
if (r-q)*(r-p) > r then R:= R, p; fi
od:
R;
CROSSREFS
Contains A338566.
Sequence in context: A245639 A362239 A147813 * A274386 A079545 A154755
KEYWORD
nonn,more
AUTHOR
Robert Israel, Nov 03 2020
STATUS
approved