A366011 G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k) * A(x)^k.

1, -3, 13, -67, 379, -2267, 14065, -89515, 580379, -3815731, 25356051, -169898467, 1145825123, -7767073859, 52858784539, -360823702851, 2468606626813, -16915880702563, 116028193869805, -796200367684945, 5463239318586601, -37465765826805457, 256664142145450777, -1755608165010431139

Offset

1,2

Comments

Reversion of g.f. for odd prime numbers together with 1.

Links

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Series Reversion

Mathematica

nmax = 24; A[_] = 0; Do[A[x_] = x - Sum[Prime[k] A[x]^k, {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
nmax = 24; CoefficientList[InverseSeries[Series[x + Sum[Prime[k] x^k, {k, 2, nmax}], {x, 0, nmax}], x], x] // Rest

Crossrefs

Cf. A006005, A007296.

Sequence in context: A242798 A239198 A234282 * A365250 A200754 A062992

Adjacent sequences: A366008 A366009 A366010 * A366012 A366013 A366014

Keyword

sign

Author

Ilya Gutkovskiy, Sep 25 2023

Status

approved