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

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.

This sequence can be expressed with the help of a general formula that uses the OEIS-indexed sequence A366997
which are the integers n such that a(n) = 3n *n3 + 2 is a prime number. This general formula is such that:

a(n) = 3^A366997 * A366997^3 + 2.

Some interesting properties of this sequence are:

◼ The next term a(8) = ∼2.20847 x10143 is too large to include in the standard OEIS format.
◼ a(9) = ∼8.66244 x10153.
◼ a(10) = ∼9.21872 x10433.
◼ This sequence is constituted by primes of the forms A002145 and A002144, with the exception of 2.
◼ The last known integer k in A366997 is 20803 and corresponds to a(13) = ∼3.21988 x109938.

The numerical data showed on this dataset was generated by the following Mathematica program:

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

The previous program was builded on Mathematica v13.3.0.

Note: More mathematical details, graphics and technical information can be found in the notebook (.nb) & pdf files provided in this data pack.

此整数序列已于2024年10月8日注册并发表在《在线整数序列百科全书》（OEIS.org）数据库中，其OEIS代码为：A376895。该序列可通过一个通用的公式来表达，该公式借助了OEIS索引序列A366997，A366997中的整数n满足条件a(n) = 3n * n^3 + 2为质数。此通用公式可表述为：a(n) = 3^A366997 * A366997^3 + 2。该序列的一些有趣性质包括：◼ 序列的第8项a(8) ≈ 2.20847 x 10^143，数值过大，无法纳入标准的OEIS格式。◼ a(9) ≈ 8.66244 x 10^153。◼ a(10) ≈ 9.21872 x 10^433。◼ 该序列由形式为A002145和A002144的质数构成，除了2以外。◼ 已知的A366997中的最后一个整数k为20803，对应a(13) ≈ 3.21988 x 10^99938。本数据集中的数值数据由以下Mathematica程序生成：Select[Table[3^k*k^3+2, {k, 0, 10000}], PrimeQ]。先前的程序是基于Mathematica v13.3.0构建的。注：更多数学细节、图形和技术信息可在提供的数据包中的笔记本(.nb)和PDF文件中找到。