<b>Extended Dataset Generated by the OEIS Integer Sequence A377045: Number of Partitions of Cuban Primes.</b>
<p dir="ltr">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.<br><br>This sequence can be expressed with the help of two general formulas that uses t...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| منشور في: |
2024
|
| الموضوعات: | |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| الملخص: | <p dir="ltr">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.<br><br>This sequence can be expressed with the help of two general formulas that uses the sequences:<br><br>1) A000041: a(n) is the number of partitions of n (the partition numbers).<br><br>2) A002407: Cuban primes: primes which are the difference of two consecutive cubes.<br><br>3) A121259: Numbers k such that (3*k^2 + 1)/4 is prime.<br><br>The two aforementioned general formulas are as follows: <br><br>a(n) = A000041(A002407(n)). <b> (1)</b><br><br>a(n) = A000041((3*A121259 (n)^2+1) / 4). <b> (2)</b><br><br>Some interesting properties of this sequence are:<br><br>◼ Number of partitions of prime numbers that are the difference of two consecutive cubes.<br><br>◼ Number of partitions of primes p such that p=(3*n^2 + 1) / 4 for some integer n (A121259).<br><br>◼ a(13) = ~1.49910(x10^43).<br><br>◼ The last known integer n in A121259 is 341 and corresponds to a(60) = ~1.59114(x10^323).<br><br>The numerical data showed on this dataset was generated by the following Mathematica program:<br><br>PartitionsP[Select[Table[(3 k^2 + 1)/4, {k, 500}], PrimeQ]] <br><br>The previous program was builded on Mathematica v13.3.0.<br><br><b>Note</b>: More mathematical details, graphics and technical information can be found in the notebook (.nb) & pdf files provided in this data pack.</p> |
|---|