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Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 is prime.
5

%I #16 Sep 08 2022 08:45:28

%S 10,30,52,70,94,120,126,142,150,160,292,318,336,378,466,792,918,960,

%T 1044,1104,1116,1180,1198,1222,1312,1446,1558,1642,1686,1780,1794,

%U 1804,1900,1902,1974,1996,2038,2040,2076,2286,2392,2428,2448,2458,2460,2478,2518,2584,2596,2602,2668,2736,2742,2788,2800

%N Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 is prime.

%H Vincenzo Librandi, <a href="/A124164/b124164.txt">Table of n, a(n) for n = 1..1000</a>

%t Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13], Print[n]], {n, 1, 300}]

%t Select[Range[8000], PrimeQ[Total[#^Range[1, 13, 2]] + 1] &] (* _Vincenzo Librandi_, Jun 28 2014 *)

%o (Magma) [n: n in [0..3000]| IsPrime(1 + n + n^3 + n^5 + n^7+ n^9 + n^11 + n^13 )]; // _Vincenzo Librandi_, Nov 12 2010

%o (Magma) [n: n in [0..3000] | IsPrime(s) where s is 1+&+[n^i: i in [1..13 by 2]]]; // _Vincenzo Librandi_, Jun 28 2014

%o (PARI) is(n)=isprime(1+n+n^3+n^5+n^7+n^9+n^11+n^13) \\ _Charles R Greathouse IV_, Feb 20 2017

%Y Cf. A049407, similar sequences listed in A244376.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Dec 13 2006