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

%I A364893 #13 Aug 27 2023 10:29:19
%S A364893 11,28,54,88,129,179,237,303,376,458,548,646,752,866,988,1118,1256,
%T A364893 1402,1558,1719,1889,2067,2253,2447,2650,2860,3078,3304,3539,3781,
%U A364893 4031,4289,4556,4830,5112,5403,5701,6007,6332,6644,6975,7313,7659,8014,8376,8747,9125
%N A364893 a(n) is the minimal positive value of m such that A325433(2m, 2n+1) > A364891(2m, 2n+1).
%H A364893 K. Banerjee and M. G. Dastidar, <a href="https://doi.org/10.35011/risc.22-20">Inequalities for the partition function arising from truncated theta series</a>, RISC Report Series No. 22-20, 2023.
%F A364893 Empirical: a(n) ~ A364894(n). (See p. 5 in Banerjee and Dastidar.)
%t A364893 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}];
%t A364893 A364891[n_, k_]:=(-1)^(k-1)*Sum[(-1)^j*(PartitionsP[n-j(2j+1)]-PartitionsP[n-(j+1)(2j+1)]), {j, 0, k-1}];
%t A364893 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
%Y A364893 Cf. A000041, A325433, A364891, A364894.
%K A364893 nonn
%O A364893 1,1
%A A364893 _Stefano Spezia_, Aug 12 2023