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A243160
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Least number k such that k^n - k^(n-1) + k^(n-2) - ... + (-1)^n is prime or 0 if no such k exists.
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1
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3, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 7, 0, 2, 0, 0, 0, 0, 0, 16, 0, 0, 0, 61, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 46, 0, 18, 0, 0, 0, 0, 0, 2, 0, 0, 0, 49, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 70
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OFFSET
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1,1
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COMMENTS
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If n is in A006093, then a(n) is not 0.
The only term where the converse is false is a(3) = 2. Also, 2 is the only such number that makes k^3 - k^2 + k - 1 prime. Otherwise, a(n) is not 0 iff n is in A006093.
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LINKS
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EXAMPLE
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1^4 - 1^3 + 1^2 - 1^1 + 1 = 1 is not prime. 2^4 - 2^3 + 2^2 - 2^1 + 1 = 11 is prime. Thus a(4) = 2.
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PROG
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(PARI) a(n)=for(k=1, 1000, s=k^n; if(ispseudoprime(s+sum(i=1, n, (-1)^i*k^(n-i))), return(k)))
n=1; while(n<100, print1(a(n), ", "); n+=1)
(PARI) A243160(n) = if(3!=n && !isprime(1+n), 0, my(s); for(k=1, oo, s=k^n; if(isprime(s+sum(i=1, n, (-1)^i*k^(n-i))), return(k)))); \\ Antti Karttunen, Jul 19 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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