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A239146
Smallest k>0 such that n +/- k and n^2 +/- k are all prime. a(n) = 0 if no such number exists.
2
0, 0, 0, 0, 0, 0, 0, 3, 2, 3, 0, 5, 0, 3, 2, 0, 0, 13, 12, 0, 2, 0, 0, 0, 6, 15, 10, 0, 12, 0, 0, 15, 20, 0, 12, 5, 0, 15, 22, 21, 12, 0, 0, 0, 14, 27, 0, 35, 0, 0, 8, 15, 0, 0, 24, 27, 0, 0, 48, 7, 48, 0, 50, 3, 6, 7, 0, 0, 28, 0, 18, 0, 0, 27, 34
OFFSET
1,8
COMMENTS
a(n) is always smaller than n due to the requirement on n-k.
LINKS
EXAMPLE
8 +/- 1 (7 and 9) and 8^2 +/- 1 (63 and 65) are not all prime. 8 +/- 2 (6 and 10) and 8^2 +/- 2 (62 and 66) are not all prime. However, 8 +/- 3 (5 and 11) and 8^2 +/- 3 (61 and 67) are all prime. Thus, a(8) = 3.
MAPLE
A239146 := proc(n)
local k ;
for k from 1 do
if n-k <= 1 then
return 0;
end if;
if isprime(n+k) and isprime(n-k) and isprime(n^2+k)
and isprime(n^2-k) then
return k;
end if;
end do;
end proc:
seq(A239146(n), n=1..80) ; # R. J. Mathar, Mar 12 2014
MATHEMATICA
a[n_] := Catch@ Block[{k = 1}, While[k < n, And @@ PrimeQ@ {n+k, n-k, n^2+k, n^2-k} && Throw@k; k++]; 0]; Array[a, 75] (* Giovanni Resta, Mar 13 2014 *)
PROG
(Python)
import sympy
from sympy import isprime
def c(n):
..for k in range(1, n):
....if isprime(n+k) and isprime(n-k) and isprime(n**2+k) and isprime(n**2-k):
......return k
n = 1
while n < 100:
..if c(n) == None:
....print(0)
..else:
....print(c(n))
..n += 1
CROSSREFS
KEYWORD
nonn
AUTHOR
Derek Orr, Mar 11 2014
STATUS
approved