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A338577 Primes p such that A013632(p)*A105161(p) > p.

%I A338577 #16 Jun 28 2024 22:23:15
%S A338577 2,3,5,7,11,13,19,23,31,47,83,89,113,199,1327
%N A338577 Primes p such that A013632(p)*A105161(p) > p.
%C A338577 Primes p such that (q-p)*(r-p) > p, where q and r are the next two primes after p.
%C A338577 a(16) > 10^8 if it exists.
%C A338577 Sequence is finite if Cramér's conjecture is true. - _Chai Wah Wu_, Nov 03 2020
%C A338577 Data from A002386 and A005250 show that a(16) > 18361375334787046697 if it exists. - _Jason Yuen_, Jun 13 2024
%e A338577 a(5) = 11 is a member because 11 is prime, the next two primes are 13 and 17, and (13-11)*(17-11) = 12 > 11.
%p A338577 p:= 0: q:=2:r:= 3: R:= NULL:
%p A338577 while p < 10^4 do
%p A338577   p:= q: q:= r: r:= nextprime(r);
%p A338577   if (q-p)*(r-p) > p then R:= R, p fi
%p A338577 od:
%p A338577 R;
%o A338577 (Python)
%o A338577 from sympy import nextprime
%o A338577 A338577_list, p, q, r = [], 2,3,5
%o A338577 while p < 10**6:
%o A338577     if (q-p)*(r-p) > p:
%o A338577         A338577_list.append(p)
%o A338577     p, q, r = q, r, nextprime(r) # _Chai Wah Wu_, Nov 03 2020
%Y A338577 Contains A338567.
%Y A338577 Cf. A013632, A105161, A338578.
%Y A338577 Cf. A002386, A005250.
%K A338577 nonn,more,hard
%O A338577 1,1
%A A338577 _Robert Israel_, Nov 03 2020