cp's OEIS Frontend

A057846 Sort the digits of n into alphabetical order (the "Obsessive Filer's Sequence").

%I A057846 #36 Aug 16 2024 21:12:20
%S A057846 0,1,2,3,4,5,6,7,8,9,10,11,12,13,41,51,16,17,81,91,20,12,22,32,42,52,
%T A057846 62,72,82,92,30,13,32,33,43,53,63,73,83,93,40,41,42,43,44,54,46,47,84,
%U A057846 49,50,51,52,53,54,55,56,57,85,59,60,16,62,63,46,56,66,76,86,96,70,17,72,73,47,57,76,77,87
%N A057846 Sort the digits of n into alphabetical order (the "Obsessive Filer's Sequence").
%C A057846 The digits of each number n (written in base 10) are put into alphabetical order by their English name. This means a given term's digits must be in this order: 8, 5, 4, 9, 1, 7, 6, 3, 2, 0. It's easy to see that any n-digit term (with digits in this order) with distinct digits, none zero, occurs exactly n! times in the sequence.
%C A057846 Since 0 = "zero" is sorted last, this works well for the English language. But the same cannot be "coded without loss" on OEIS for languages where the name for 0 is not sorted last: E.g., in German, 0="null" comes before, e.g., 2="zwei", which would yield "02" for 20, but leading zeros are not allowed on the OEIS. - _M. F. Hasler_, Jul 28 2013
%C A057846 See A225805 for the French version. - _M. F. Hasler_, Jul 28 2013
%D A057846 M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002), p. 1.
%H A057846 Ivan Neretin, <a href="/A057846/b057846.txt">Table of n, a(n) for n = 0..10000</a>
%H A057846 Michael Halm, <a href="http://michaelhalm.tripod.com/id109.htm">Sequences (Re)discovered</a>, retrieved on July 28, 2013
%e A057846 a(14)=41 because the digits of 14, 1 (one) and 4 (four), are in alphabetical order when arranged as 4, then 1, so 41.
%t A057846 s = {9, 4, 8, 7, 2, 1, 6, 5, 0, 3}; Table[FromDigits[Sort[IntegerDigits[n], s[[#1 + 1]] < s[[#2 + 1]] &]], {n, 78}] (* _Ivan Neretin_, Jul 09 2015 *)
%o A057846 (PARI) A057846(n,o=[9, 4, 8, 7, 2, 1, 6, 5, 0, 3])= {sum(i=1,#n=vecsort(digits(n),(a,b)->o[b+1]-o[a+1]),n[i]*10^i)/10} \\ - _M. F. Hasler_, Jul 28 2013
%o A057846 (Python)
%o A057846 def k(c): return "8549176320".index(c)
%o A057846 def a(n): return int("".join(sorted(str(n), key=k)))
%o A057846 print([a(n) for n in range(100)]) # _Michael S. Branicky_, Aug 17 2022
%Y A057846 Cf. A072809, A225805 (in French).
%K A057846 base,nonn,word,look,easy
%O A057846 0,3
%A A057846 _Rick L. Shepherd_, Jul 23 2002
%E A057846 Edited by _N. J. A. Sloane_, Aug 31 2006
%E A057846 Original terms 76, 86, 96 restored by _Rick L. Shepherd_, Jul 26 2013