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Search: id:A123977
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| A123977 |
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Numbers n in base 10 whose base 10 expansion of n^2 is the same as if n were interpreted in some base b>10 and n^2 also calculated in that base. |
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+0
1
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| 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 30, 31, 100, 101, 102, 103
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The list is clearly infinite as a 1 followed by any number of zeros is a member.
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EXAMPLE
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13^2 = 169 (base 10), but (b+3)^2 = b^2 + 6b + 9, so 13 is in the list. 14^2 = 196 (base 10), but it is not true in general that (b+4)^2 = b^2 + 9b + 6, so 14 is not in the list.
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CROSSREFS
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Cf. A061909.
Sequence in context: A055655 A007090 A102859 this_sequence A069967 A061909 A159952
Adjacent sequences: A123974 A123975 A123976 this_sequence A123978 A123979 A123980
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KEYWORD
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base,nonn
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AUTHOR
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Andrew Silberman (sandrew(AT)math.upenn.edu), Oct 30 2006
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