Journal of Integer Sequences, Vol. 24 (2021), Article 21.7.1

Fagan's Construction, Strange Roots, and Tchoukaillon Solitaire

Mark Dukes
School of Mathematics and Statistics
University College Dublin
Dublin 4


We examine a procedure that, on starting with an integer n, results in a pair of equal integers that are no greater than n. We call the resulting value the strange root of n, and we show how this strange-root-finding procedure is intimately linked to the game of Tchoukaillon solitaire. We analyze the strange-root-finding procedure in reverse to determine when a prescribed value is the strange root of at most two integers. We present a conjecture about strange roots and translate this conjecture into one involving Tchoukaillon solitaire.

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(Concerned with sequences A002491 A185001 A204539 A204540.)

Received November 4 2020; revised versions received April 22 2021; May 14 2021; May 26 2021. Published in Journal of Integer Sequences, June 4 2021.

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