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 A241071 Numbers n such that k^n + (k-1)^n + ... + 3^n + 2^n is prime for some k. 0
 1, 2, 4, 6, 8, 10, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It is known that a(n) is even for all n (except a(1)). See A241070 for more restrictions on a(n). It is known that 16, 24, 32, 36, 42, 48, 56, 60, 66, 72, 80, 108, 110, 120, 144, and 192 are all members of this sequence. LINKS Table of n, a(n) for n=1..7. EXAMPLE There exists a k such that k^2 + (k-1)^2 + ... + 3^2 + 2^2 is prime (let k = 3). Thus, 2 is a member of this sequence. There exists a k such that k^4 + (k-1)^4 + ... + 3^4 + 2^4 is prime (let k = 3). Thus, 4 is a member of this sequence. However, there does not exist a k such that k^3 + (k-1)^3 + ... + 3^3 + 2^3 is prime (this is tested for k < 7500). Thus, 3 is not a member of this sequence. PROG (PARI) a(n)=for(k=1, 7500, if(ispseudoprime(sum(i=2, k, i^n)), return(k))) n=1; while(n<250, if(a(n), print(n)); n+=1) CROSSREFS Sequence in context: A334614 A185449 A096922 * A353026 A356431 A345444 Adjacent sequences: A241068 A241069 A241070 * A241072 A241073 A241074 KEYWORD nonn,hard,more AUTHOR Derek Orr, Apr 15 2014 STATUS approved

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Last modified September 17 18:39 EDT 2024. Contains 375990 sequences. (Running on oeis4.)