|
| |
|
|
A219222
|
|
Numbers that can be expressed as the sum of 2 positive squares but not as the sum of 3 positive squares.
|
|
2
|
|
|
|
2, 5, 8, 10, 13, 20, 25, 32, 37, 40, 52, 58, 80, 85, 100, 128, 130, 148, 160, 208, 232, 320, 340, 400, 512, 520, 592, 640, 832, 928, 1280, 1360, 1600, 2048, 2080, 2368, 2560, 3328, 3712, 5120, 5440, 6400, 8192, 8320, 9472, 10240, 13312, 14848, 20480, 21760
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Among these numbers a(n), some of them are not divisible by 4: 2, 5, 10, 13, 25, 37, 58, 85, 130. All members of the sequence can be expressed as a(n) = 4^k*a0, with a0 taken in the set described above, that is A051952 except 1.
Subsequence of A000549. - Chai Wah Wu, Feb 05 2016
|
|
|
LINKS
|
Donovan Johnson, Table of n, a(n) for n = 1..120 (terms <= 10^9)
P. K. J. Draxl, Sommes de deux carrés qui ne sont pas sommes de trois carrés., Mémoires de la SMF, tome 37 (1974), p. 53-53.
|
|
|
FORMULA
|
Empirical g.f.: -x*(2*x^16 +28*x^15 +20*x^14 +33*x^13 +40*x^12 +26*x^11 +32*x^10 +32*x^9 +37*x^8 +32*x^7 +25*x^6 +20*x^5 +13*x^4 +10*x^3 +8*x^2 +5*x +2) / (4*x^9 -1). - Colin Barker, Sep 23 2014
|
|
|
PROG
|
(Python)
limit = 21760
squares_lst = [i*i for i in range(1, int(limit**0.5)+2) if i*i <= limit]
squares_set = set(squares_lst)
def sum2squares(n):
for s in squares_lst:
if n - s in squares_set: return True
if n - s < 0: return False
alst = []
for m in range(2, limit+1):
if sum2squares(m):
sum3 = False
for s in squares_lst:
if sum2squares(m - s): sum3 = True; break
if m - s < 0: break
if not sum3: alst.append(m)
print(alst) # Michael S. Branicky, Feb 05 2021
|
|
|
CROSSREFS
|
Cf. A000404, A000549, A051952.
Sequence in context: A070216 A100829 A030713 * A263831 A189457 A189362
Adjacent sequences: A219219 A219220 A219221 * A219223 A219224 A219225
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Michel Marcus, Nov 16 2012
|
|
|
STATUS
|
approved
|
| |
|
|
