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A268236
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Fouriest transform of n: write n in that base b >= 4 which maximizes the number of 4's; in case of a tie pick the smallest b; sequence gives n in base b.
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10
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0, 1, 2, 3, 4, 11, 12, 13, 20, 14, 14, 14, 14, 14, 24, 14, 24, 14, 24, 34, 40, 41, 42, 43, 44, 41, 42, 43, 44, 104, 42, 43, 44, 45, 114, 43, 44, 45, 46, 124, 44, 45, 46, 47, 44, 140, 141, 142, 44, 144, 46, 47, 44, 104, 204, 47, 44, 49, 134, 214, 44, 141, 142, 143, 144, 145
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OFFSET
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0,3
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COMMENTS
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If no base b gives any 4's then we take b=4.
For n>65 "digits" greater than 9 appear in a(n) - see the first link. This explains why this sequence has no b-file: the OEIS restriction to decimal digits means that a(66) cannot be written as a single base-10 number (it would be "4,10").
The Fouriest transform pun suggests (by analogy with shaky, shakier, shakiest) investigating the Foury, Fourier, and Fouriest numbers. Three obvious candidates for the Foury numbers are A011534, A019764, and A268544, which are all "Foury" in different ways.
With respect to a fixed base b, we could say that n is Fourier than m (in base b) if the fraction [or number?] of 4's in the representation of n (base b) is greater than the analogous quantity for m. But it is not clear which definition is to be preferred. In base 10, which is Fourier, 440 or 439454?
This sequence and its companions were created during a dinner following the Experimental Mathematics Seminar at Rutgers University on Feb 04 2016.
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LINKS
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Zach Weinersmith, Fouriest number, SMBC (Saturday Morning Breakfast Cereal) column, Feb 01, 2013.
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EXAMPLE
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For n=24, the base-5 representation of 24 is 44. So the Fouriest transform of 24 is a(24) = 44, which uses base b = A268237(24) = 5 and contains A268238(24) = 2 4's.
The Fouriest transform of n=66 is 4,10 in base b=14 (note the non-decimal digit) and contains a single 4.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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