A196153 Primes of the form 2*n^3 + 5*n^2 + 3*n + 1.

11, 43, 109, 631, 953, 2531, 3301, 5279, 9521, 13339, 15581, 18061, 38611, 43093, 70753, 77419, 99901, 108263, 180181, 205391, 218833, 247451, 262651, 294893, 329671, 407219, 472751, 496063, 520129, 544961, 652189, 942943, 1056241, 1095931, 1178269, 1309351, 1355113, 1815841

Offset

1,1

Comments

A rational number is created by 1/n + 1/n^2 + 1/(n+1) + 1/(n+1)^2 and has a reduced numerator of 2*n^3 + 5*n^2 + 3*n + 1.

From n=1 to 100, 38 primes, 48 semiprimes, and 14 numbers requiring three or more prime factors were created. This is very anomalous compared to the expected distribution of such numbers from 1 to 2050301.

Links

Table of n, a(n) for n=1..38.

Example

For n=37, 2*37^3 + 5*37^2 + 3*37 + 1 = 108263, a prime.

Mathematica

Select[Table[2n^3+5n^2+3n+1, {n, 100}], PrimeQ] (* Harvey P. Dale, Jan 21 2014 *)

Crossrefs

Sequence in context: A141086 A352966 A142039 * A213763 A302226 A201714

Adjacent sequences: A196150 A196151 A196152 * A196154 A196155 A196156

Keyword

nonn

Author

J. M. Bergot, Sep 28 2011

Extensions

Entries corrected by R. J. Mathar, Sep 28 2011

Status

approved