|
|
A011539
|
|
"9ish numbers": decimal representation contains at least one nine.
|
|
56
|
|
|
9, 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 119, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 209, 219, 229, 239, 249, 259, 269, 279, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The 9ish numbers are closed under lunar multiplication. The lunar primes (A087097) are a subset.
Almost all numbers are 9ish, in the sense that the asymptotic density of this set is 1: Among the 9*10^(n-1) n-digit numbers, only a fraction of 0.8*0.9^(n-1) doesn't have a digit 9, and this fraction tends to zero (< 1/10^k for n > 22k-3). This explains the formula a(n) ~ n. - M. F. Hasler, Nov 19 2018
A 9ish number is a number whose largest decimal digit is 9. - Stefano Spezia, Nov 16 2023
|
|
LINKS
|
D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
|
|
FORMULA
|
|
|
EXAMPLE
|
E.g. 9, 19, 69, 90, 96, 99 and 1234567890 are all 9ish.
|
|
MAPLE
|
seq(`if`(numboccur(9, convert(n, base, 10))>0, n, NULL), n=0..100); # François Marques, Oct 12 2020
|
|
MATHEMATICA
|
Select[ Range[ 0, 100 ], (Count[ IntegerDigits[ #, 10 ], 9 ]>0)& ] (* François Marques, Oct 12 2020 *)
Select[Range[300], DigitCount[#, 10, 9]>0&] (* Harvey P. Dale, Mar 04 2023 *)
|
|
PROG
|
(Haskell)
a011539 n = a011539_list !! (n-1)
(GAP) Filtered([1..300], n->9 in ListOfDigits(n)); # Muniru A Asiru, Feb 25 2019
(Python)
def ok(n): return '9' in str(n)
|
|
CROSSREFS
|
Cf. A088924 (number of n-digit terms).
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|