|
|
A173330
|
|
First of two intermediate sequences for integral solution of A002144(n)=x^2+y^2.
|
|
4
|
|
|
1, 10, 1, 5, 1, 5, 46, 5, 70, 5, 9, 1, 106, 106, 126, 142, 146, 13, 9, 186, 1, 214, 13, 226, 1, 13, 9, 5, 17, 13, 306, 9, 5, 17, 366, 17, 378, 1, 406, 406, 17, 442, 21, 442, 5, 510, 21, 538, 13, 1, 570, 5, 17, 598, 25, 13, 25, 650, 1, 5, 694, 706, 9, 742, 25, 17, 786, 5, 25
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
REFERENCES
|
H. Davenport, The Higher Arithmetic (Cambridge University Press 7th ed., 1999), ch. V.3, p.122.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (2k)! / 2(k!)^2 mod p, where p = 4*k+1 = A002144(n).
|
|
EXAMPLE
|
a(7) = 26! / (2*(13!)^2) mod 53 = 403291461126605635584000000/77551576087265280000 mod 53 = 5200300 mod 53 = 46,
a(8) = 30! / (2*(15!)^2) mod 61 = 265252859812191058636308480000000/3420024505448398848000000 mod 61 = 77558760 mod 61 = 5,
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|