A268236 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.

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

Offset: 0

Author

Jake Baron, Patrick Devlin, Nathan Fox, and N. J. A. Sloane, Feb 06 2016

Keywords

• nonn
• base

Comments

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.

Examples

			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.
		

Links

• Nathan Fox, First 10000 terms of A268236, A268237, A268238. Square brackets are used to separate the "digits" of A268236, since for n >= 66 these can be greater than 10.
• Zach Weinersmith, Fouriest number, SMBC (Saturday Morning Breakfast Cereal) column, Feb 01, 2013.

Crossrefs

Cf. A268237 (the base b), A268238 (number of 4's).

See A268540 and A268541 for the "44" entries.

See also the "Foury" numbers A011534, A019764, and A268544.

A268360 and A349031 are other Foury sequences.