Prime Triangle
المؤلف:
Guy, R. K
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
10-1-2021
947
Prime Triangle
A triangle with rows containing the numbers ![<span style=]()
{1,2,...,n}" src="https://mathworld.wolfram.com/images/equations/PrimeTriangle/Inline1.gif" style="height:15px; width:69px" /> that begins with 1, ends with 
, and such that the sum of each two consecutive entries being a prime. Rows 2 to 6 are unique,
(OEIS A051237) but there are multiple possibilities starting with row 7. For example, the two possibilities for row 7 are ![<span style=]()
{1,4,3,2,5,6,7}" src="https://mathworld.wolfram.com/images/equations/PrimeTriangle/Inline3.gif" style="height:15px; width:107px" /> and ![<span style=]()
{1,6,5,2,3,4,7}" src="https://mathworld.wolfram.com/images/equations/PrimeTriangle/Inline4.gif" style="height:15px; width:107px" />. The number of possible rows ending with 
, 2, ..., are 0, 1, 1, 1, 1, 1, 2, 4, 7, 24, 80, ... (OEIS A036440).
REFERENCES:
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 106, 1994.
Kenney, M. J. "Student Math Notes." NCTM News Bulletin. Nov. 1986.
Sloane, N. J. A. Sequences A036440 and A051237 in "The On-Line Encyclopedia of Integer Sequences."
الاكثر قراءة في نظرية الاعداد
اخر الاخبار
اخبار العتبة العباسية المقدسة
