Extended Dataset Generated by the OEIS Integer Sequence A377045: Number of Partitions of Cuban Primes.

This integer sequence was registered and published in the On-Line Encyclopedia of Integer Sequences (OEIS.org) Database on October 14 - 2024, under the OEIS code: A377045.

This sequence can be expressed with the help of two general formulas that uses the sequences:

1) A000041: a(n) is the number of partitions of n (the partition numbers).

2) A002407: Cuban primes: primes which are the difference of two consecutive cubes.

3) A121259: Numbers k such that (3*k^2 + 1)/4 is prime.

The two aforementioned general formulas are as follows:

a(n) = A000041(A002407(n)). (1)

a(n) = A000041((3*A121259 (n)^2+1) / 4). (2)

Some interesting properties of this sequence are:

◼ Number of partitions of prime numbers that are the difference of two consecutive cubes.

◼ Number of partitions of primes p such that p=(3*n^2 + 1) / 4 for some integer n (A121259).

◼ a(13) = ~1.49910(x10^43).

◼ The last known integer n in A121259 is 341 and corresponds to a(60) = ~1.59114(x10^323).

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

PartitionsP[Select[Table[(3 k^2 + 1)/4, {k, 500}], 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.