<b>Extended Dataset Generated by the OEIS Integer Sequence A376895: Primes of the Form 3^k*k^3 </b><b>+ 2.</b>

This integer sequence was registered and published in the On-Line Encyclopedia of Integer Sequences (OEIS.org) Database on October 08 - 2024, under the OEIS code: A376895.<br><br>This sequence can be expressed with the help of a general formula that uses the OEIS-indexed sequence A366997<br>which are the integers n such that a(n) = 3n *n3 + 2 is a prime number. This general formula is such that:<br><br>a(n) = 3^A366997 * A366997^3 + 2.<br><br>Some interesting properties of this sequence are:<br><br>◼ The next term a(8) = ∼2.20847 x10143 is too large to include in the standard OEIS format.<br>◼ a(9) = ∼8.66244 x10153.<br>◼ a(10) = ∼9.21872 x10433.<br>◼ This sequence is constituted by primes of the forms A002145 and A002144, with the exception of 2.<br>◼ The last known integer k in A366997 is 20803 and corresponds to a(13) = ∼3.21988 x109938.<br><br>The numerical data showed on this dataset was generated by the following Mathematica program:<br><br>Select[Table[3^k*k^3+2, {k, 0, 10000}], PrimeQ]<br><br>The previous program was builded on Mathematica v13.3.0.<br><br><b><i>Note</i></b>: More mathematical details, graphics and technical information can be found in the notebook (.nb) &amp; pdf files provided in this data pack.