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A365310
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a(n) = 2^(2^n) + 2^(2^(n+1)-1).
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0
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4, 12, 144, 33024, 2147549184, 9223372041149743104, 170141183460469231750134047789593657344, 57896044618658097711785492504343953926975274699741220483192166611388333031424
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OFFSET
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0,1
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COMMENTS
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a(n) is the long leg of the Pythagorean triangle whose short leg is the n-th Fermat number, A000215(n), and whose hypotenuse is a(n) + 1.
[A000215(n), a(n), a(n) + 1] is a primitive Pythagorean triple of the form [2*k + 1, 2*k^2 + 2*k, 2*k^2 + 2*k + 1] where k = A058891(n).
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LINKS
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FORMULA
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a(n) = sqrt(Integral_{x=1..A000215(n)} (x^3-x) dx).
sqrt(a(n) + (a(n)+1)) = sqrt((a(n)+1)^2 - a(n)^2) = A000215(n).
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MATHEMATICA
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PROG
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(Python)
for n in range(0, 8):
print(2**(2**n)+2**(2**(n+1)-1))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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