

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

Table of n, a(n) for n=1..71.
Index entries for sequences related to the Josephus Problem


FORMULA

a(1) = 1, a(2) = 1, a(n) = (a(n2) + 3) (mod n) if (a(n2) + 3) (mod n) is not 0; a(n) = n if (a(n2) + 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(n2) + 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



