

A235264


Tileable numbers: base2 representation, considered as a fixed disconnected polyomino, tiles all places >= 0.


3



1, 3, 5, 7, 9, 15, 17, 21, 31, 33, 51, 63, 65, 73, 85, 127, 129, 195, 255, 257, 273, 341, 455, 511, 513, 585, 771, 819, 1023, 1025, 1057, 1285, 1365, 2047, 2049, 3075, 3591, 3855, 4095, 4097, 4161, 4369, 4681, 5461
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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 2adic m = 1/n exists and 2adic product m*n involves no carries.
Conjecturally, a(n) = (2^k1)/m where k, m >= 1, and base2 product m*a(n) involves no carries. Confirmed for a(n) <= 2^20.
Conjecturally, a(n) is of the form PROD 2^(d_i*b_i)1)/(2^b_i1) 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 2adic definition.  Charlie Neder, Nov 04 2018
Second conjecture is true, see Neder link.  Charlie Neder, Dec 04 2018


EXAMPLE

n = 3855 has 2adic representation .10100000101, and negative reciprocal repeating 2adic m = .(1100110000000000)... The 2adic product n*m = 1 = .(1)... involves no carries, so n is tileable.


CROSSREFS

Conjecturally, subset of A006995 (base2 palindromes).
Sequence in context: A006995 A163410 A329419 * A064896 A076188 A265852
Adjacent sequences: A235261 A235262 A235263 * A235265 A235266 A235267


KEYWORD

nonn,nice


AUTHOR

David W. Wilson, Jan 05 2014


STATUS

approved



