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A231354
Least k such that n - triangular(k) is a square, or -1 if no such k exists.
1
0, 0, 1, 2, 0, 1, 3, 2, -1, 0, 1, 4, 2, -1, 4, 3, 0, 1, -1, 2, -1, 6, 3, -1, 5, 0, 1, -1, 2, 7, 6, 3, 7, -1, -1, 4, 0, 1, -1, 2, 5, -1, 3, -1, 7, 8, 4, -1, -1, 0, 1, 5, 2, 7, 9, 3, 10, 6, -1, 4, -1, 8, -1, -1, 0, 1, 11, 2, -1, -1, 3, 10, 8, -1, 4, 11, -1, 7, 12, 5, 10, 0
OFFSET
0,4
COMMENTS
Indices of -1's: A014134.
Indices of 0's: A000290.
Indices of 1's: A002522.
PROG
(Python)
import math
for n in range(333):
for k in range(1000000):
t = n - k*(k+1)/2
if t<0:
print('-1', end=', ')
break
r = int(math.sqrt(t))
if r*r==t:
print(str(k), end=', ')
break
CROSSREFS
KEYWORD
sign
AUTHOR
Alex Ratushnyak, Nov 08 2013
STATUS
approved