

A057846


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


6



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
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OFFSET

0,3


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 ndigit 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


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


EXAMPLE

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.


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 *)


PROG

(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


CROSSREFS

Cf. A072809.
Sequence in context: A323175 A323204 A072763 * A055647 A043318 A044915
Adjacent sequences: A057843 A057844 A057845 * A057847 A057848 A057849


KEYWORD

base,nonn,word,look,easy


AUTHOR

Rick L. Shepherd, Jul 23 2002


EXTENSIONS

Edited by N. J. A. Sloane, Aug 31 2006
Original terms 76, 86, 96 restored by Rick L. Shepherd, Jul 26 2013


STATUS

approved



