A354425 List of k such that sign(A009277(k)) = sign(A009277(k+1)).

0, 2, 6, 10, 16, 22, 29, 37, 45, 54, 63, 73, 83, 93, 104, 116, 128, 140, 153, 166, 179, 193, 207, 221, 236, 251, 266, 282, 298, 314, 331, 347, 364, 382, 399, 417, 435, 454, 473, 491, 511, 530, 550, 570, 590, 610, 631, 652, 673, 694, 715, 737, 759, 781, 804, 826, 849, 872, 895, 919, 942, 966, 990

Offset

1,2

Comments

What is the limit of a(n) / n^(3/2) ?

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..182

Example

2 is in the sequence because A009277(2) = -4 and A009277(3) = -88 have the same sign.
6 is in the sequence because A009277(6) = 675776 and A009277(7) = 903834752 have the same sign.

Mathematica

nmax = 500; A009277 = Table[(CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[k]], {k, 3, 2*nmax, 2}]; Join[{0}, Select[Range[nmax-2], A009277[[#]]*A009277[[#+1]] > 0 &]]
With[{nn=2000}, SequencePosition[Sign[Take[CoefficientList[Series[Exp[Tanh[x]^2], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]], {x_, x_}]][[;; , 1]]-1 (* Harvey P. Dale, Apr 08 2023 *)

Crossrefs

Cf. A009277, A354246, A354399.

Sequence in context: A032426 A220453 A195957 * A294013 A183575 A096184

Adjacent sequences: A354422 A354423 A354424 * A354426 A354427 A354428

Keyword

nonn

Author

Vaclav Kotesovec, May 27 2022, following a suggestion from Paul D. Hanna

Status

approved