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 A337191 If cards numbered 1 through n are "Down Two Table" shuffled (top two put on bottom one at a time, third from top card dealt to table) until all of the cards are placed on the table, a(n) is the number of the last card dealt. 0
 1, 1, 1, 4, 4, 1, 7, 4, 1, 7, 4, 10, 7, 13, 10, 16, 13, 1, 16, 4, 19, 7, 22, 10, 25, 13, 1, 16, 4, 19, 7, 22, 10, 25, 13, 28, 16, 31, 19, 34, 22, 37, 25, 40, 28, 43, 31, 46, 34, 49, 37, 52, 40, 1, 43, 4, 46, 7, 49, 10, 52, 13, 55, 16, 58, 19, 61, 22, 64, 25, 67 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS This sequence is related to the Josephus Problem, which can be modeled with the Australian Under Down Shuffle, one card placed under the deck, one card laid down on the table until all the cards are on the table. LINKS FORMULA a(1) = 1, a(2) = 1, a(n) = (a(n-2) + 3) (mod n) if (a(n-2) + 3) (mod n) is not 0; a(n) = n if (a(n-2) + 3) (mod n)=0. Any number n can be written as either 2*(3^k) + 2m (where 0 <= m < 3^k, k = 0,1,2,...) or 3^k + 2m (where 0 <= m < 3^k, k = 0,1,2,...), in either case a(n) = 3m + 1. PROG (PARI) a(n) = if (n <= 2, 1, my(x = (a(n-2) + 3) % n); if (x, x, n)); \\ Michel Marcus, Aug 20 2020 CROSSREFS Cf. A006257. Sequence in context: A247252 A016495 A335826 * A341863 A047213 A128213 Adjacent sequences:  A337188 A337189 A337190 * A337192 A337193 A337194 KEYWORD nonn AUTHOR Robert W. Vallin, Aug 18 2020 EXTENSIONS More terms from Michel Marcus, Aug 20 2020 STATUS approved

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Last modified September 18 20:58 EDT 2021. Contains 347536 sequences. (Running on oeis4.)