A309388 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.
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
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..1000 from Robert Israel)
Programs
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Maple
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: select(filter, [$1..300]); # Robert Israel, Aug 06 2019
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Mathematica
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] -
Python
from sympy import integer_nthroot A309388_list, y, w = [], 1, 0 while len(A309388_list) < 10000: w += y z = 0 for x in range(1,y+1): z += x if integer_nthroot(8*(w+z)+1,2)[1]: break else: A309388_list.append(y) y += 1 # Chai Wah Wu, Aug 07 2019
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