A354399 List of k such that sign(A009273(k)) = sign(A009273(k+1)).

0, 1, 5, 12, 21, 33, 47, 64, 83, 105, 129, 155, 184, 216, 250, 286, 325, 366, 410, 456, 505, 556, 610, 666, 725, 786, 849, 915, 984, 1055, 1128, 1204, 1282, 1363, 1446, 1532, 1620, 1711, 1804, 1900, 1998, 2098, 2201, 2307, 2415, 2525, 2638, 2753, 2871, 2991, 3114, 3239, 3367, 3497, 3630, 3765, 3903, 4043, 4185, 4330, 4477, 4627, 4780, 4935

Offset: 1

Author

Vaclav Kotesovec, May 25 2022

Keywords

• nonn

Comments

Conjecture: lim_{n->oo} a(n)/n^2 = Pi^2/8 = A111003 = 1.2337...

Examples

			12 is in the sequence because A009273(12) = -454930757753597952 and A009273(13) = -94991612229069430784 have the same sign.
		

Crossrefs

Cf. A009273, A354246, A354425.

Programs

Mathematica

nmax = 400; A009273 = Table[(CoefficientList[Series[E^(x*Tanh[x]), {x, 0, 2*nmax}], x]*Range[0, 2*nmax]!)[[k]], {k, 1, 2*nmax, 2}]; Join[{0}, Select[Range[nmax-1], A009273[[#]]*A009273[[#-1]] > 0 &] - 1]