OFFSET
1,1
COMMENTS
This is similar to A239146; however, here the numbers listed are the n values for which k != 0.
It is very likely that k does not exist for most n values since k < n for all n. Thus, only the numbers n with some such k (depending on n) are listed.
EXAMPLE
n = 1,2,3,...11 do not have a k such that n +/- k, n^2 +/- k, and n^3 +/- k are all prime. However, for n = 12, 12 +/- 5 (7 and 17), 12^2 +/- 5 (139 and 149) and 12^3 +/- 5 (1723 and 1733) are all prime. So 12 is a member of this sequence.
MAPLE
isA239147 := proc(n)
local k ;
for k from 1 do
if n-k <= 1 then
return false;
end if;
if isprime(n+k) and isprime(n-k) and isprime(n^2+k)
and isprime(n^2-k) and isprime(n^3+k) and isprime(n^3-k) then
return true;
end if;
end do;
end proc:
for n from 1 to 800 do
if isA239147(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Mar 12 2014
PROG
(Python)
import sympy
from sympy import isprime
def c(n):
..for k in range(n):
....if isprime(n+k) and isprime(n-k) and isprime(n**2+k) and isprime(n**2-k) and isprime(n**3+k) and isprime(n**3-k):
......return k
n = 1
while n < 10**3:
..if c(n) != None:
....print(n)
..n += 1
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Mar 11 2014
STATUS
approved