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%I #17 Sep 08 2022 08:45:28
%S 1,186,256,325,763,853,916,1239,1297,1398,1500,1669,1878,1992,2373,
%T 2503,2536,2578,2626,2740,2823,2836,2841,2926,2958,3193,3255,3381,
%U 3447,3738,3843,3903,4095,4156,4246,4321,4407,4530,4540,4572,4855,5190,5322,5361,5530
%N Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^53 + n^55 is prime.
%H Vincenzo Librandi, <a href="/A124207/b124207.txt">Table of n, a(n) for n = 1..270</a>
%p a:= proc(n) option remember; local k;
%p for k from 1+ a(n-1) while
%p not isprime(1+(k^57-k)/(k^2-1)) do od; k
%p end: a(1):=1:
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Jun 26 2014
%t Do[If[PrimeQ[1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 + n^21 + n^23 + n^25 + n^27 + n^29 + n^31 + n^33 + n^35 + n^37 + n^39 + n^41 + n^43 + n^45 + n^47 + n^49 + n^51 + n^53 + n^55], Print[n]],{n, 1, 2400}]
%t Select[Range[6000], PrimeQ[Total[#^Range[1, 55, 2]] + 1] &] (* _Vincenzo Librandi_, Jun 28 2014 *)
%o (PARI) for(n=1,10^4,if(ispseudoprime(sum(i=0,27,n^(2*i+1))+1),print1(n,", "))) \\ _Derek Orr_, Jun 24 2014
%o (Magma) [n: n in [0..6000] | IsPrime(s) where s is 1+&+[n^i: i in [1..55 by 2]]]; // _Vincenzo Librandi_, Jun 28 2014
%Y Cf. A049407, similar sequences listed in A244376.
%K nonn,easy
%O 1,2
%A _Artur Jasinski_, Dec 13 2006
%E a(42) and beyond from _Derek Orr_, Jun 24 2014
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