Heptagonal Triangular Number
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A039835, A046193, and A046194 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
17-12-2020
1232
Heptagonal Triangular Number
A number which is simultaneously a heptagonal number 
and triangular number 
. Such numbers exist when
 |
(1)
|
Completing the square and rearranging gives
 |
(2)
|
Substituting 
and 
gives the Pell-like quadratic Diophantine equation
 |
(3)
|
which has basic solutions 
, (7, 3), and (18, 8). Additional solutions can be obtained from the unit Pell equation, and correspond to integer solutions when 
, (5, 10), (221, 493), (1513, 3382), ... (OEIS A046193 and A039835), corresponding to the heptagonal triangular numbers 1, 55, 121771, 5720653, 12625478965, ... (OEIS A046194).
REFERENCES:
Sloane, N. J. A. Sequences A039835, A046193, and A046194 in "The On-Line Encyclopedia of Integer Sequences."
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