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
KEYWORD
nonn
AUTHOR
Rafael Parra Machio, Jun 18 2011
STATUS
approved