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A235264
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Tileable numbers: base-2 representation, considered as a fixed disconnected polyomino, tiles all places >= 0.
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3
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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
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1,2
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LINKS
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FORMULA
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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
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EXAMPLE
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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.
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CROSSREFS
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Conjecturally, subset of A006995 (base-2 palindromes).
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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