A239147 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.

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

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.

Links

Table of n, a(n) for n=1..50.

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

Cf. A239146.

Sequence in context: A323195 A033165 A224676 * A136739 A186620 A042851

Adjacent sequences: A239144 A239145 A239146 * A239148 A239149 A239150

Keyword

nonn

Author

Derek Orr, Mar 11 2014

Status

approved