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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 (list; graph; refs; listen; history; text; internal format)
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 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

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

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)