Queue sieves: the Seidov rearrangement, Tchoukaillon solitaire, and Gamma-function constants for Josephus-type sieves

Seidov's rearrangement (OEIS A104706) takes the queue 1, 2, 3, ... and repeatedly moves its front element x to 2x places further right. Knuth observed in 2021 that the positions of its records are half the Tchoukaillon numbers A002491; Cloitre (2007) and Fagan and Chandler (2012) recorded two further unexplained identities. We prove all three by one lemma: for every nondecreasing displacement rule x -> D(x) the queue process coincides with a Mancala-type solitaire in which hole x is refilled with D(x) - x + 1 stones, the board being the left-inversion table of the queue permutation. The first-appearance times of the queue are then given by a nested sieve, which yields closed formulas for the other sequences of Seidov (A104737, A104739). For these "Tchoukaillon-type" sieves and for the "Flavius-type" sieves of our earlier paper we establish exact dual recursions of the same shape (conjugate partitions) and prove a growth law with an error term: if the moduli grow like cx, the n-th term equals C n^((c+1)/c) + O(n^((c+1)^2/(c(2c+1)))), where C is the product of two Gamma-function constants, one for each of the two dual sieves. For c = 1 this is the n^2/pi law of Erdős and Jabotinsky and the pi n^2/4 law of Andersson, with their error exponent 4/3; for the sieve that deletes every (2k+1)-th entry at step k (A399807) the constant is 2*3^(-3/2)*Gamma(2/3)^(3/2)/Gamma(3/2) = 0.68436...