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
(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
CROSSREFS
KEYWORD
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