OFFSET
1,2
LINKS
Charlie Neder, Table of n, a(n) for n = 1..2314 (First 701 terms from David W. Wilson)
Charlie Neder, Proof of characterization of this sequence
Allan Wechsler, A possible characterization of A125121 (Original idea)
FORMULA
Numbers n such that 2-adic m = -1/n exists and 2-adic product m*n involves no carries.
Conjecturally, a(n) = (2^k-1)/m where k, m >= 1, and base-2 product m*a(n) involves no carries. Confirmed for a(n) <= 2^20.
Conjecturally, a(n) is of the form Product (2^(d_i*b_i)-1)/(2^b_i-1) where d_i >= 1, b_i >= 2, and d_i*b_i | d_(i+1). Confirmed for a(n) <= 2^20.
First conjecture is equivalent to the 2-adic definition. - Charlie Neder, Nov 04 2018
Second conjecture is true, see Neder link. - Charlie Neder, Dec 04 2018
EXAMPLE
n = 3855 has 2-adic representation .10100000101, and negative reciprocal repeating 2-adic m = .(1100110000000000)... The 2-adic product n*m = -1 = .(1)... involves no carries, so n is tileable.
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
David W. Wilson, Jan 05 2014
STATUS
approved