This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A268236 #32 Mar 25 2025 12:53:34 %S A268236 0,1,2,3,4,11,12,13,20,14,14,14,14,14,24,14,24,14,24,34,40,41,42,43, %T A268236 44,41,42,43,44,104,42,43,44,45,114,43,44,45,46,124,44,45,46,47,44, %U A268236 140,141,142,44,144,46,47,44,104,204,47,44,49,134,214,44,141,142,143,144,145 %N 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. %C A268236 If no base b gives any 4's then we take b=4. %C A268236 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"). %C A268236 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. %C A268236 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? %C A268236 This sequence and its companions were created during a dinner following the Experimental Mathematics Seminar at Rutgers University on Feb 04 2016. %H A268236 Nathan Fox, <a href="/A268236/a268236_10000.txt">First 10000 terms of A268236, A268237, A268238</a>. Square brackets are used to separate the "digits" of A268236, since for n >= 66 these can be greater than 10. %H A268236 Zach Weinersmith, <a href="http://www.smbc-comics.com/?id=2874">Fouriest number</a>, SMBC (Saturday Morning Breakfast Cereal) column, Feb 01, 2013. %e A268236 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. %e A268236 The Fouriest transform of n=66 is 4,10 in base b=14 (note the non-decimal digit) and contains a single 4. %Y A268236 Cf. A268237 (the base b), A268238 (number of 4's). %Y A268236 See A268540 and A268541 for the "44" entries. %Y A268236 See also the "Foury" numbers A011534, A019764, and A268544. %Y A268236 A268360 and A349031 are other Foury sequences. %K A268236 nonn,base %O A268236 0,3 %A A268236 _Jake Baron_, _Patrick Devlin_, _Nathan Fox_, and _N. J. A. Sloane_, Feb 06 2016