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A239147
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Numbers n such that there exists a k>0 such that all six of n +/- k, n^2 +/- k, and n^3 +/- k are prime.
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0
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12, 25, 29, 36, 45, 55, 78, 87, 105, 109, 111, 130, 140, 141, 155, 160, 190, 196, 209, 216, 231, 245, 246, 265, 274, 280, 289, 294, 311, 315, 329, 356, 364, 385, 409, 441, 444, 465, 475, 489, 494, 531, 535, 572, 582, 600, 624, 629, 650, 665
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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;
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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