A101685 First differences of A101684.
1, -1, 3, 1, -1, 3, 1, -1, 3, 1, -2, 4, 1, -2, 4, 1, -1, 3, 1, -1, 3, 1, -3, 5, 1, -3, 5, 1, -1, 3, 1, -1, 3, 1, -2, 4, 1, -2, 4, 1, -1, 3, 1, -1, 3, 1, -4, 6, 1, -4, 6, 1, -1, 3, 1, -1, 3, 1, -2, 4, 1, -2, 4, 1, -1, 3, 1, -1, 3, 1, -3, 5, 1, -3, 5, 1, -1, 3, 1, -1, 3, 1, -2, 4, 1, -2, 4
Offset: 0
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Programs
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Mathematica
Differences[IntegerExponent[Denominator[With[{nn = 80}, CoefficientList[Series[Exp[-1 + Sqrt[1 + x]], {x, 0, nn}], x] Range[0, nn]!]], 2]] (* Wesley Ivan Hurt, May 26 2024 after Harvey P. Dale *)
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