5 deleted 65 characters in body
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Python 3, 7284 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5)%4==1for i in range(n)])or n in[0,1]

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Note : after some further test, I realized my submission doesn't work for 0 and 1.Try it online!

Python 3, 72 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5)%4==1for i in range(n)])

Try it online!

Note : after some further test, I realized my submission doesn't work for 0 and 1.

Python 3, 84 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5)%4==1for i in range(n)])or n in[0,1]

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4 deleted 7 characters in body
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Python 3, 7672 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5-1)/2%2==0for%4==1for i in range(n)])

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Note : after some further test, I realized my submission doesn't work for 0 and 1.

Python 3, 76 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5-1)/2%2==0for i in range(n)])

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Python 3, 72 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5)%4==1for i in range(n)])

Try it online!

Note : after some further test, I realized my submission doesn't work for 0 and 1.

3 deleted 8 characters in body
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Python 3, 8076 bytes

lambda n:1in set([(math.sqrt(8*(n+(i*(i+1)/2)*3)+1)**0.5-1)/2%1==0for2%2==0for i in range(n)])

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Python 3, 80 bytes

lambda n:1in set([(math.sqrt(8*(n+(i*(i+1)/2)*3)+1)-1)/2%1==0for i in range(n)])

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Python 3, 76 bytes

lambda n:1in set([((8*(n+(i*(i+1)/2)*3)+1)**0.5-1)/2%2==0for i in range(n)])

Try it online!

2 added 332 characters in body
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1
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