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%I #15 Jan 05 2021 15:04:40
%S 17,563,67559,758677727,5639788283,12519315713,228317617103,
%T 2215267259747,2458514680949,5331791014853,9754511753219,
%U 11469661520567,60568409162663,64329745367417,148696534573127,164890314104507,1843608625927967,2182930574787737,5990875533026939
%N Primes of the form (n-1)^6 + n^5 + (n+1)^4.
%C 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.
%H Robert Israel, <a href="/A191865/b191865.txt">Table of n, a(n) for n = 1..10000</a>
%H Rafael Parra Machío, <a href="http://hojamat.es/parra/prop2011.pdf">PROPIEDADES DEL 2011: Un paseo a través de los números primos</a>
%e 2^6 + 3^5 + 4^4 = 563 and 6^6 + 7^5 + 8^4 = 67559 are primes in the sequence.
%p R:= NULL: count:= 0:
%p for n from 1 by 2 while count < 100 do
%p v:= (n-1)^6+n^5+(n+1)^4;
%p if isprime(v) then count:= count+1; R:= R,v; fi
%p od:
%p R; # _Robert Israel_, Jan 05 2021
%t lst={};Do[If[PrimeQ[p=(n-1)^6+n^5+(n+1)^4], AppendTo[lst, p]],{n,200}];lst
%t lst={};Do[If[PrimeQ[p=n^6-5n^5+16n^4-16n^3+21n^2-2n+2], AppendTo[lst, p]],{n,200}];lst
%o (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
%K nonn
%O 1,1
%A _Rafael Parra Machio_, Jun 18 2011
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