A364893 a(n) is the minimal positive value of m such that A325433(2m, 2n+1) > A364891(2m, 2n+1).

11, 28, 54, 88, 129, 179, 237, 303, 376, 458, 548, 646, 752, 866, 988, 1118, 1256, 1402, 1558, 1719, 1889, 2067, 2253, 2447, 2650, 2860, 3078, 3304, 3539, 3781, 4031, 4289, 4556, 4830, 5112, 5403, 5701, 6007, 6332, 6644, 6975, 7313, 7659, 8014, 8376, 8747, 9125

Offset

1,1

Links

Table of n, a(n) for n=1..47.

K. Banerjee and M. G. Dastidar, Inequalities for the partition function arising from truncated theta series, RISC Report Series No. 22-20, 2023.

Formula

Empirical: a(n) ~ A364894(n). (See p. 5 in Banerjee and Dastidar.)

Mathematica

A325433[n_, k_]:=(-1)^(k-1)*Sum[(-1)^j*(PartitionsP[n-j*(3*j+1)/2]-PartitionsP[n-j*(3*j+5)/2-1]), {j, 0, k-1}];
A364891[n_, k_]:=(-1)^(k-1)*Sum[(-1)^j*(PartitionsP[n-j(2j+1)]-PartitionsP[n-(j+1)(2j+1)]), {j, 0, k-1}];
nmax=47; a={}; For[n=1, n<=nmax, n++, m=1; While[A325433[2m, 2n+1]<=A364891[2m, 2n+1], m++]; AppendTo[a, m]]; a

Crossrefs

Cf. A000041, A325433, A364891, A364894.

Sequence in context: A336335 A140677 A264443 * A349660 A242941 A018944

Adjacent sequences: A364890 A364891 A364892 * A364894 A364895 A364896

Keyword

nonn

Author

Stefano Spezia, Aug 12 2023

Status

approved