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A309388
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Numbers y such that x*(x+1) + y*(y+1) = z*(z+1) does not have a solution in positive integers x, z with x <= y.
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1
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1, 3, 4, 7, 8, 11, 12, 15, 16, 19, 23, 28, 31, 32, 36, 40, 43, 47, 52, 59, 60, 63, 64, 67, 71, 72, 79, 83, 87, 88, 96, 100, 103, 107, 108, 112, 127, 128, 131, 136, 139, 148, 151, 156, 163, 167, 172, 176, 179, 180, 183, 187, 191, 192, 196, 199, 211, 223, 227
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OFFSET
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1,2
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COMMENTS
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The similar sequence A027861 (complement of A012132) is related to primes.
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LINKS
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MAPLE
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filter:= proc(y) local S;
S:= map(t -> subs(t, x), [isolve(x*(x+1)+y*(y+1)=z*(z+1))]);
select(t -> t>0 and t<=y, S) = []
end proc:
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MATHEMATICA
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max = 500; lst = {}; For[x = 1, x < max, x++,
For[y = x, y < max, y++,
For[z = y, z < max, z++,
If[x (x + 1) + y (y + 1) == z (z + 1),
lst = AppendTo[lst, y]]]]]; lst =
Select[Union[lst], # < max/2 &]; Complement[Range[Length[lst]], lst]
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PROG
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(Python)
from sympy import integer_nthroot
w += y
z = 0
for x in range(1, y+1):
z += x
if integer_nthroot(8*(w+z)+1, 2)[1]:
break
else:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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