A216440 a(n) = smallest m such that 2n-1 | 2^m+1, or 0 if no such m exists.

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

Offset

1,3

Comments

From Kristjan Kiolein, Mar 25 2023: (Start)

Conjecture: a(n) is the number of riffle shuffles of 2(n-1) 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 in-shuffle 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 out-shuffle variant of the riffle shuffle, e.g., [1, 2, 3, 4] -> [1, 3, 2, 4] -> [1, 2, 3, 4]. (End)

Links

V. Raman, Table of n, a(n) for n = 1..100.

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

Cf. A002326.

Sequence in context: A285310 A262946 A343932 * A094720 A334495 A155800

Adjacent sequences: A216437 A216438 A216439 * A216441 A216442 A216443

Keyword

nonn

Author

V. Raman, Sep 07 2012

Status

approved