OFFSET
1,1
COMMENTS
A variant of A162989, which is the main entry. - N. J. A. Sloane, Aug 12 2009
Note that p+1 = r-1. Thus, the sequence describes twin primes whose immediate neighbors are not cubefree. - Tanya Khovanova, Aug 22 2021
EXAMPLE
69497 and 69499 twin primes. Moreover, 69496 is divisible by 2^3, 69498 is divisible by 3^3, and 69500 is divisible by 5^3. Thus, 69497 and 69499 are in the sequence. - Tanya Khovanova, Aug 22 2021
MATHEMATICA
s=Select[Prime@Range[200000], PrimeQ[#+2]&&Min[Max[Last/@FactorInteger[#]]&/@{#-1, #+1, #+3}]>2&]; Sort@Join[s, s+2] (* Giorgos Kalogeropoulos, Aug 22 2021 *)
PROG
(Python)
from sympy import nextprime, factorint
def cubefree(n): return max(e for e in factorint(n).values()) <= 2
def auptop(limit):
alst, p, r = [], 3, 5
while p < limit:
if r - p == 2 and not any(cubefree(i) for i in [p-1, p+1, r+1]):
alst.extend([p, r])
p, r = r, nextprime(p)
return alst
print(auptop(2*10**6)) # Michael S. Branicky, Aug 22 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jul 15 2009
EXTENSIONS
Terms corrected by Zak Seidov, Jul 19 2009
Edited by N. J. A. Sloane, Aug 12 2009
STATUS
approved