A155562 revision #15
|
| |
|
|
A155562
|
|
Intersection of A001481 and A002479: N = a^2 + b^2 = c^2 + 2d^2 for some integers a,b,c,d.
|
|
2
|
|
|
|
0, 1, 2, 4, 8, 9, 16, 17, 18, 25, 32, 34, 36, 41, 49, 50, 64, 68, 72, 73, 81, 82, 89, 97, 98, 100, 113, 121, 128, 136, 137, 144, 146, 153, 162, 164, 169, 178, 193, 194, 196, 200, 225, 226, 233, 241, 242, 256, 257, 272, 274, 281, 288, 289, 292, 306, 313, 324, 328
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Contains A155561 as a subsequence (obtained by restricting a,b,c,d to be nonzero). Also contains A000290 (squares) and A001105 (twice the squares) as subsequence.
N is also of the form x^2 - 2y^2.
N = (p^2-q^2-2*r*s)^2+(r^2-s^2-2*p*q)^2
= (p^2+q^2-r^2-s^2)^2+2*(p*r-p*s-q*r-q*s)^2
= (p^2+q^2+r^2+s^2)^2-2*(p*r+p*s+q*r-q*s)^2
for some nonnegative integers p, q, r, s. (End)
|
|
|
LINKS
|
|
|
|
PROG
|
(PARI) isA155562(n, /* use optional 2nd arg to get other analogous sequences */c=[2, 1]) = { for(i=1, #c, for(b=0, sqrtint(n\c[i]), issquare(n-c[i]*b^2) & next(2)); return); 1}
for( n=1, 500, isA155562(n) & print1(n", "))
(Python)
from itertools import count, islice
from sympy import factorint
def A155562_gen(): # generator of terms
return filter(lambda n:all((p & 3 != 3 and p & 7 < 5) or e & 1 == 0 for p, e in factorint(n).items()), count(0))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
