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%I #11 Apr 02 2014 11:56:13
%S 2,3,4,5,6,7,8,12,13,16,17,19,31,34,48,61,68,72,89,107,112,124,127,
%T 236,260,288,384,396,432,520,521,576,607,1080,1244,1279,1424,1500,
%U 1660,2203,2281,2640,2730,2808,3190,3217,4150,4253,4423,4428,5016,5892
%N Numbers n such that k^n-(k-1)^n-...-3^n-2^n-1 is prime for some k.
%C These are the values of n such that A240081(n) is nonzero.
%o (Python)
%o import sympy
%o from sympy import isprime
%o def Leq(n):
%o ..for k in range(1000):
%o ....num = k**n
%o ....for i in range(2, k):
%o ......num -= i**n
%o ......if num < 1:
%o ........return None
%o ....if isprime(num-1):
%o ......return k
%o n = 1
%o while n < 10**3:
%o ..if Leq(n) != None:
%o ....print(n)
%o ..n += 1
%o (PARI) f(n)=for(k=1,10^3,num=k^n;for(i=2,k-1,num-=i^n;if(num<1,return(0)));if(ispseudoprime(num-1),return(k))); n=1; while(n<10^3,if(f(n),print(n));n+=1)
%Y Cf. A240081.
%K nonn
%O 1,1
%A _Derek Orr_, Mar 31 2014
%E a(34)-a(52) from _Giovanni Resta_, Apr 02 2014
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