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A113918
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Cardinality of Image^inf({ 2 }) under repeated base-n zero-split squaring.
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2
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OFFSET
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2,1
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COMMENTS
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Define f_b(x) to be the set of base b numbers left after splitting x^2 at its zero digits and Image_b(S) = union_{x in S}{ { x } union f_b(S) }, then a(n) = | Image_n^inf({ 2 }) |.
Conjecture: a(n) is finite for all n.
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LINKS
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EXAMPLE
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f_10(29648) = { 4, 39, 879 } since 29648^2 = 879003904.
a(8) = 2 since Image_8({ 2 }) = { 2, 4 } and f_8({ 2, 4 }) = { 2, 4 } and |{ 2, 4 }| is 2.
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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