A087176 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.

5, 6, 9, 9, 9, 10, 11

Offset

2,1

Comments

I can prove a(n) < n+4 and am certain that a(n)=n+3 for n>6, but cannot prove it.

References

Michael Golomb, "Prime numbers and Irreducible Polynomials", in a forthcoming issue (in 2003) of Mathematics Magazine

Links

Table of n, a(n) for n=2..8.

Example

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.

Crossrefs

Sequence in context: A332327 A260635 A306016 * A227006 A139454 A049329

Adjacent sequences: A087173 A087174 A087175 * A087177 A087178 A087179

Keyword

hard,nonn

Author

Michael Golomb (mgolomb(AT)math.purdue.edu), Oct 19 2003

Status

approved