login
A127206
Numbers k such that k^j + (k+1)^j is prime for j = 1, 2, 4, 8.
1
1, 765, 39269, 70260, 71399, 85764, 100079, 167789, 218229, 307020, 388449, 468945, 514760, 553400, 568904, 782595, 826284, 1160199, 1220430, 1403775, 1633020, 1714739, 1727930, 1788144, 1932900, 1958705, 2023119, 2037450, 2178804, 2185520, 2193969, 2238474, 2264774
OFFSET
1,2
COMMENTS
k^j + (k+1)^j is prime only for j = power of 2.
Subset of A128780 which is a subset of A068501.
LINKS
EXAMPLE
{765 + 766, 765^2 + 766^2, 765^4 + 766^4, 765^8 + 766^8} = {1531, 1171981, 686770904161, 235828747162526935093921}, all prime.
MATHEMATICA
Do[If[PrimeQ[2n + 1] && PrimeQ[n^2 + (n+1)^2] && PrimeQ[n^4 + (n+1)^4] && PrimeQ[n^8 + (n+1)^8], Print[n]], {n, 5*10^6}] (* Ryan Propper, Mar 30 2007 *)
PROG
(Magma) [n: n in [1..3*10^6]| IsPrime(2*n+1) and IsPrime(n^2+(n+1)^2) and IsPrime(n^4+(n+1)^4) and IsPrime(n^8+(n+1)^8)]; // Vincenzo Librandi, Nov 18 2018
CROSSREFS
Sequence in context: A124413 A319741 A329757 * A343704 A343705 A247486
KEYWORD
nonn
AUTHOR
Zak Seidov, Mar 28 2007
EXTENSIONS
More terms from Ryan Propper, Mar 30 2007
STATUS
approved