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A235264 Tileable numbers: base-2 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 (list; graph; refs; listen; history; text; internal format)
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 PROD 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

Conjecturally, subset of A006995 (base-2 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

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Last modified October 27 06:31 EDT 2021. Contains 348271 sequences. (Running on oeis4.)