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%I #13 Jun 12 2014 21:22:30
%S 1,2,4,8,16,1440
%N Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n + 1 is prime for some k.
%C These terms have k-values {2, 2, 2, 2, 2, 5} respectively. When k = 2, the prime mentioned in the definition is given in A164307. - _Derek Orr_, Jun 06 2014
%e 1^1 + 2^1 = 3 is prime (k = 2).
%e 1^2 + 2^2 = 5 is prime (k = 2).
%e 1^4 + 2^4 = 17 is prime (k = 2).
%e 1^8 + 2^8 = 257 is prime (k = 2).
%e 1^16 + 2^16 = 65537 is prime (k = 2).
%e 1^1440 + 2^1440 + 3^1440 + 4^1440 + 5^1440 = 3.287049497374559048967261852*10^1006 = 3287049497374559048967261852 ... 458593539025033893379 is prime (k = 5).
%t lst={};Do[s=0;Do[If[PrimeQ[s+=n^x],AppendTo[lst,x];Print[Date[],x]],{n,4!}],{x,7!}];lst
%o (PARI) a(n)=for(k=1,10^3,if(ispseudoprime(sum(i=1,k,i^n)),return(k)))
%o n=1;while(n<5000,if(a(n),print1(n,", "));n++) \\ _Derek Orr_, Jun 06 2014
%Y Cf. A000215, A070592, A019434, A092506, A093179, A100270, A123599, A164307.
%K nonn,hard,more
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Aug 12 2009
%E Definition improved by _Derek Orr_, Jun 06 2014
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