

A216440


a(n) = smallest m such that 2n1  2^m+1, or 0 if no such m exists.


1



1, 1, 2, 0, 3, 5, 6, 0, 4, 9, 0, 0, 10, 9, 14, 0, 5, 0, 18, 0, 10, 7, 0, 0, 0, 0, 26, 0, 9, 29, 30, 0, 6, 33, 0, 0, 0, 0, 0, 0, 27, 41, 0, 0, 0, 0, 0, 0, 24, 15, 50, 0, 0, 53, 18, 0, 14, 0, 0, 0, 55, 0, 50, 0, 7, 65, 0, 0, 34, 69, 0, 0, 14, 0, 74, 0, 0, 0, 26, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Conjecture: a(n) is the number of riffle shuffles of 2(n1) cards required to reverse the order of the deck, or 0 if no such number of shuffles exists.
The number of shuffles required to reverse the deck is A002326(n)/2 when a(n) != 0 and n != 1.
This conjecture is in the context of the inshuffle variant of the riffle shuffle, e.g., [1, 2, 3, 4] > [3, 1, 4, 2] > [4, 3, 2, 1].
This does not apply in the context of the outshuffle variant of the riffle shuffle, e.g., [1, 2, 3, 4] > [1, 3, 2, 4] > [1, 2, 3, 4]. (End)


LINKS



PROG

(PARI) for(i=0, 200, i++; m=0; for(x=1, i, if(((2^x+1))%i==0, m=x; break)); print1(m", ")) \\ V. Raman, Nov 22 2012


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



