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

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, 62, 72, 82, 92, 30, 13, 32, 33, 43, 53, 63, 73, 83, 93, 40, 41, 42, 43, 44, 54, 46, 47, 84, 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

Offset: 0

Author

Rick L. Shepherd, Jul 23 2002

Keywords

• base
• nonn
• word
• look
• easy

Comments

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.

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

See A225805 for the French version. - M. F. Hasler, Jul 28 2013

Examples

			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.
		

References

• M. J. Halm, Sequences (Re)discovered, Mpossibilities 81 (Aug. 2002), p. 1.

Links

• Ivan Neretin, Table of n, a(n) for n = 0..10000
• Michael Halm, Sequences (Re)discovered, retrieved on July 28, 2013

Crossrefs

Cf. A072809, A225805 (in French).

Programs

Mathematica

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 *)

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

Python

def k(c): return "8549176320".index(c)
def a(n): return int("".join(sorted(str(n), key=k)))
print([a(n) for n in range(100)]) # Michael S. Branicky, Aug 17 2022

Extensions

Edited by N. J. A. Sloane, Aug 31 2006

Original terms 76, 86, 96 restored by Rick L. Shepherd, Jul 26 2013