A319116 Signs of the Maclaurin coefficients of 1/(exp(x) + Pi/2).

1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1

Offset

0

Links

Table of n, a(n) for n=0..74.

Formula

Conjecture: a(n) is the same as the sign of cos((n+1)*arctan(Pi/log(Pi/2))). We can also use arctan(Pi/log(Pi/2))/Pi ~ 1/2 ~ 5/11 ~ 3776/8307 ~ 3781/8318 and so on. If the numerator is odd, we have, for example, a(n) = -a(n+2) or a(n) = -a(n+11) with some counterexamples. For even numerators we have, for example, a(n) = a(n+8307), also with some counterexamples.

Example

a(1) = -a(12) = a(23) = -1.

Maple

S:= series(1/(exp(x)+Pi/2), x, 147):
seq(signum(coeff(S, x, j)), j=0..146);

Mathematica

Sign[CoefficientList[Series[1/(Exp[x] + Pi/2), {x, 0, 100}], x]] (* G. C. Greubel, Oct 31 2018 *)

Prog

(PARI) apply(x->sign(x), Vec(1/(exp(x+O(x^100)) + Pi/2))) \\ Michel Marcus, Sep 13 2018

Crossrefs

Cf. A210245, A210247.

Sequence in context: A210245 A210247 A256175 * A337004 A343785 A359738

Adjacent sequences: A319113 A319114 A319115 * A319117 A319118 A319119

Keyword

sign

Author

Mikhail Kurkov, Sep 10 2018 [verification needed]

Status

approved