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A049409
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Numbers n such that n^4 + n^3 + n^2 + n + 1 is prime.
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2
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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; internal format)
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OFFSET
| 1,2
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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
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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MATHEMATICA
| lst={}; Do[p=n^0+n^1+n^2+n^3+n^4; If[PrimeQ[p], AppendTo[lst, n]], {n, 300}]; lst (* From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 10 2009 *)
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PROG
| (PARI) for(n=1, 1000, ispseudoprime(n^4+n^3+n^2+n+1) & print1(n", ")) \\ - M. F. Hasler, Feb 09 2012
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CROSSREFS
| Sequence in context: A110949 A126343 A174539 * A190548 A187971 A190486
Adjacent sequences: A049406 A049407 A049408 * A049410 A049411 A049412
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KEYWORD
| nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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