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

Author

Rafael Parra Machio, Jun 18 2011

Keywords

• nonn

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.

Examples

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

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

Programs

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

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