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A106275
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Numbers k for which the absolute value of the discriminant of the polynomial x^k - x^(k-1) - ... - x - 1 is a prime times 2^m for some m >= 0.
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1
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2, 3, 4, 5, 6, 7, 21, 26, 99, 158, 405
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OFFSET
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1,1
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COMMENTS
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This polynomial is the characteristic polynomial of the Fibonacci and Lucas k-step recursions. Are the k-step recursions different -- in some way -- for the values of k that yield a prime*2^m discriminant? No other k < 10000.
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LINKS
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PROG
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(PARI) f(n) = poldisc('x^n-sum(k=0, n-1, 'x^k)); \\ A106273
isok(k) = my(x=abs(f(k))); ispseudoprime(x) || ispseudoprime(x/2^valuation(x, 2)); \\ Michel Marcus, Mar 26 2024
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CROSSREFS
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Cf. A106273 (discriminant of the polynomial x^n - x^(n-1) - ... - x - 1).
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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