A191865 Primes of the form (n-1)^6 + n^5 + (n+1)^4.

17, 563, 67559, 758677727, 5639788283, 12519315713, 228317617103, 2215267259747, 2458514680949, 5331791014853, 9754511753219, 11469661520567, 60568409162663, 64329745367417, 148696534573127, 164890314104507, 1843608625927967, 2182930574787737, 5990875533026939

Offset

1,1

Comments

Sum of three consecutive numbers using exponents 6, 5, and 4 to generate prime numbers from n^6 - 5n^5 + 16n^4 - 16n^3 + 21n^2 - 2n + 2 = (n-1)^6 + n^5 + (n+1)^4.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Rafael Parra Machío, PROPIEDADES DEL 2011: Un paseo a través de los números primos

Example

2^6 + 3^5 + 4^4 = 563 and 6^6 + 7^5 + 8^4 = 67559 are primes in the sequence.

Maple

R:= NULL: count:= 0:
for n from 1 by 2 while count < 100 do
   v:= (n-1)^6+n^5+(n+1)^4;
   if isprime(v) then count:= count+1; R:= R, v; fi
od:
R; # Robert Israel, Jan 05 2021

Mathematica

lst={}; Do[If[PrimeQ[p=(n-1)^6+n^5+(n+1)^4], AppendTo[lst, p]], {n, 200}]; lst
lst={}; Do[If[PrimeQ[p=n^6-5n^5+16n^4-16n^3+21n^2-2n+2], AppendTo[lst, p]], {n, 200}]; lst

Prog

(PARI) forstep(n=1, 1e3, 2, if(isprime(k=(n-1)^6+n^5+(n+1)^4), print1(k", "))) \\ Charles R Greathouse IV, Jun 19 2011

Crossrefs

Sequence in context: A197395 A280181 A012069 * A249862 A056771 A041547

Adjacent sequences: A191862 A191863 A191864 * A191866 A191867 A191868

Keyword

nonn

Author

Rafael Parra Machio, Jun 18 2011

Status

approved