<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.

本整数序列于2024年10月8日登记并发表于在线整数序列百科（On-Line Encyclopedia of Integer Sequences，OEIS.org）数据库，其OEIS编号为A376895。

该序列可借助编号为A366997的OEIS索引序列推导得到，其中A366997为使得a(n)=3n·n³+2为素数的整数n，其通用形式为：

a(n) = 3^A366997 · A366997³ + 2。

本序列具有如下有趣性质：

◼ 第8项a(8) ≈ 2.20847 × 10^143，数值过大，无法纳入标准OEIS数据库格式；
◼ a(9) ≈ 8.66244 × 10^153；
◼ a(10) ≈ 9.21872 × 10^433；
◼ 本序列由形如A002145与A002144的素数构成，仅不含素数2；
◼ 目前已知的A366997序列中最大整数k为20803，对应第13项a(13) ≈ 3.21988 × 10^9938。

本数据集所展示的数值由以下Mathematica程序生成：

Select[Table[3^k*k^3 + 2, {k, 0, 10000}], PrimeQ]

该程序基于Mathematica v13.3.0版本编写。

**注**：更多数学细节、图表与技术信息可参阅本数据包中附带的笔记本（.nb）与PDF文件。

搜集汇总

背景与挑战

背景概述

该数据集是OEIS整数序列A376895的扩展数据集，专注于形如3^k*k^3 + 2的素数。它基于序列A366997生成，包含大数值素数项（如a(8)约2.20847×10^143），并通过Mathematica程序计算得出，适用于组合数学、数论和数值计算领域的研究。