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Search: id:A087176
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| A087176 |
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a(n) - 1 is the maximal number of integers for which the absolute value of a reducible polynomial with integral coefficients of degree n is a prime. |
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1
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OFFSET
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2,1
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COMMENT
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I can prove a(n) < n+4 and am certain that a(n)=n+3 for n>6, but cannot prove it.
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REFERENCES
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Michael Golomb, "Prime numbers and Irreducible Polynomials", in a forthcoming issue (in 2003) of Mathematics Magazine
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EXAMPLE
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a(3)=6 because the polynomial (x^2 -x -1)( 6x + 11) equals 5,-11,-17,23,-5 at the integers -1,0,1,2,-2 resp., but no reducible polynomial of degree 3 can be of absolute value a prime at 6 integers.
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CROSSREFS
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Sequence in context: A019598 A118261 A021641 this_sequence A049329 A117827 A134736
Adjacent sequences: A087173 A087174 A087175 this_sequence A087177 A087178 A087179
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KEYWORD
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hard,nonn
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AUTHOR
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Michael Golomb (mgolomb(AT)math.purdue.edu), Oct 19 2003
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