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A049409 Numbers n such that n^4 + n^3 + n^2 + n + 1 is prime. 35
1, 2, 7, 12, 13, 17, 22, 23, 24, 28, 29, 30, 40, 43, 44, 50, 62, 63, 68, 73, 74, 77, 79, 83, 85, 94, 99, 110, 117, 118, 120, 122, 127, 129, 134, 143, 145, 154, 162, 164, 165, 172, 175, 177, 193, 198, 204, 208, 222, 227, 239, 249, 254, 255, 260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There is no square > 1 in this sequence, because if f(n) = n^4 + n^3 + n^2 + n + 1, then f(n^2) = f(n)*f(-n). Actually, f(x) divides f(x^m) for all m not in 5Z. So the only perfect powers in this sequence can be 5th, 25th, 125th... powers. The least perfect power > 1 in this sequence is 22^5. - M. F. Hasler, Feb 09 2012

The corresponding prime numbers n^4 + n^3 + n^2 + n + 1 are in A088548. - Bernard Schott, Dec 19 2012

This is also the list of bases where 11111 is a prime number. - Christian N. K. Anderson, Mar 28 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

MAPLE

A049409:=n->if isprime(n^4+n^3+n^2+n+1) then n fi; seq(A049409(n), n=1..300); # Wesley Ivan Hurt, Dec 28 2013

MATHEMATICA

lst={}; Do[p=n^0+n^1+n^2+n^3+n^4; If[PrimeQ[p], AppendTo[lst, n]], {n, 300}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 10 2009 *)

Select[Range[300], PrimeQ[1+Total[#^Range[4]]]&] (* Harvey P. Dale, Mar 12 2018 *)

PROG

(PARI) for(n=1, 1000, ispseudoprime(n^4+n^3+n^2+n+1) & print1(n", "))  \\ M. F. Hasler, Feb 09 2012

CROSSREFS

Cf. A088548.

Sequence in context: A226703 A126343 A174539 * A287580 A326231 A190548

Adjacent sequences:  A049406 A049407 A049408 * A049410 A049411 A049412

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 18 13:30 EST 2020. Contains 331007 sequences. (Running on oeis4.)