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A191865 Primes of the form (n-1)^6 + n^5 + (n+1)^4. 0
17, 563, 67559, 758677727, 5639788283, 12519315713, 228317617103, 2215267259747, 2458514680949, 5331791014853, 9754511753219, 11469661520567, 60568409162663 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..13.

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.

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

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)