Prime Constant
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A010051, A051006, A051007, A102878, and A103313 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
5-10-2020
1088
Prime Constant
The characteristic function
![f(n)=<span style=]() {1 n is prime; 0 n otherwise " src="https://mathworld.wolfram.com/images/equations/PrimeConstant/NumberedEquation1.gif" style="height:41px; width:143px" /> |
(1)
|
of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for 
, 2, .... The constant obtained by concatenating these digits and interpreting them as a binary fraction is therefore
(OEIS A051006).
The continued fraction is [0, 2, 2, 2, 3, 12, 131, 1, ...] (OEIS A051007). It has high-water marks of 0, 2, 3, 12, 131, 169, ... (OEIS A102878), occurring at positions 0, 1, 4, 5, 6, 20, 31, 54, ... (OEIS A103313).
REFERENCES:
Sloane, N. J. A. Sequences A010051, A051006, A051007, A102878, and A103313 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
