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A271637
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Squared-squares in base 2: numbers n such that n^2 in base 2 is of the form xx for a string x.
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1
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6, 820, 104391567, 119304648, 858993460, 900719925474100, 26202761468337432, 29478106651879611, 32753451835421790, 225701339254799219773, 243062980735937621294, 260424622217076022815, 277786263698214424336, 944473296573929042740, 232485734541274841289650
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OFFSET
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1,1
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COMMENTS
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The base-2 expansion must be canonical (not start with leading zeros).
The sequence is infinite, as (4/5)*(2^(20*k + 10) + 1) has the property for k >= 0.
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REFERENCES
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Andrew Bridy, Robert J. Lemke Oliver, Arlo Shallit, and Jeffrey Shallit, The Generalized Nagell-Ljunggren Problem: Powers with Repetitive Representations, Experimental Math, 28 (2019), 428-439.
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LINKS
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EXAMPLE
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The number 6 is in the sequence because 36 = 6^2 and 36 in base 2 is 100100, which is xx for x = 100.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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