A105400 Absolute values of the three roots of p^3 + 2*p^2 - (3 - b[n])*p - b[n]: b[n]=3*Prime[n]-Prime[n]^2.

2, 1, 1, 3, 0, 1, 5, 1, 2, 7, 1, 4, 11, 1, 8, 13, 1, 10, 17, 1, 14, 19, 1, 16, 23, 1, 20, 29, 1, 26, 31, 1, 28, 37, 1, 34, 41, 1, 38, 43, 1, 40, 47, 1, 44, 53, 1, 50, 59, 1, 56, 61, 1, 58, 67, 1, 64, 71, 1, 68, 73, 1, 70, 79, 1, 76, 83, 1, 80, 89, 1, 86, 97, 1, 94, 101, 1, 98, 103, 1, 100

Offset

1,1

Comments

The maximum modulus root of this polynomial is always a prime.

Links

Table of n, a(n) for n=1..81.

Formula

b[n]=3*Prime[n]-Prime[n]^2 a(n) = Abs[root[i, m]]/.p^3 + 2*p^2 - (3 - b[n])*p - b[n]

Mathematica

b= Table[3* Prime[n] - Prime[n]^2, {n, 1, Digits}] a = Abs[Flatten[Table[p /. Solve[p^3 + 2*p^2 - (3 - b[[n]])*p - b[[n]] == 0, p][[i]], {n, 1, Digits}, {i, 1, 3}]]]

Crossrefs

Sequence in context: A155726 A325687 A230079 * A194516 A299235 A341259

Adjacent sequences: A105397 A105398 A105399 * A105401 A105402 A105403

Keyword

nonn

Author

Roger L. Bagula, May 01 2005

Status

approved