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

2, 3, 5, 7, 11, 13, 19, 23, 31, 47, 83, 89, 113, 199, 1327

Offset

1,1

Comments

Primes p such that (q-p)*(r-p) > p, where q and r are the next two primes after p.

a(16) > 10^8 if it exists.

Sequence is finite if Cramér's conjecture is true. - Chai Wah Wu, Nov 03 2020

Data from A002386 and A005250 show that a(16) > 18361375334787046697 if it exists. - Jason Yuen, Jun 13 2024

Links

Table of n, a(n) for n=1..15.

Example

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.

Maple

p:= 0: q:=2:r:= 3: R:= NULL:
while p < 10^4 do
  p:= q: q:= r: r:= nextprime(r);
  if (q-p)*(r-p) > p then R:= R, p fi
od:
R;

Prog

(Python)
from sympy import nextprime
A338577_list, p, q, r = [], 2, 3, 5
while p < 10**6:
    if (q-p)*(r-p) > p:
        A338577_list.append(p)
    p, q, r = q, r, nextprime(r) # Chai Wah Wu, Nov 03 2020

Crossrefs

Contains A338567.

Cf. A013632, A105161, A338578.

Cf. A002386, A005250.

Sequence in context: A092581 A362527 A130807 * A030145 A285983 A020588

Adjacent sequences: A338574 A338575 A338576 * A338578 A338579 A338580

Keyword

nonn,more,hard

Author

Robert Israel, Nov 03 2020

Status

approved