

A011539


"9ish numbers": decimal representation contains at least one nine.


37



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
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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^(n1) ndigit numbers, only a fraction of 0.8*0.9^(n1) doesn't have a digit 9, and this fraction tends to zero (< 1/10^k for n > 22k3). This explains the formula a(n) ~ n.  M. F. Hasler, Nov 19 2018


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]
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]
Index entries for sequences related to dismal (or lunar) arithmetic
Index entries for 10automatic sequences.


FORMULA

Complement of A007095. A102683(a(n)) > 0 (defines this sequence). A068505(a(n)) = a(n)): fixed points of A068505 are the terms of this sequence and the numbers < 9.  Reinhard Zumkeller, Dec 29 2011, edited by M. F. Hasler, Nov 16 2018
a(n) ~ n.  Charles R Greathouse IV, May 15 2013


EXAMPLE

E.g. 9, 19, 69, 90, 96, 99 and 1234567890 are all 9ish.


PROG

(Haskell)
a011539 n = a011539_list !! (n1)
a011539_list = filter ((> 0) . a102683) [1..]  Reinhard Zumkeller, Dec 29 2011
(PARI) is(n)=n=vecsort(digits(n)); n[#n]==9 \\ Charles R Greathouse IV, May 15 2013
(PARI) select( is_A011539(n)=vecmax(digits(n))==9, [1..300]) \\ M. F. Hasler, Nov 16 2018
(GAP) Filtered([1..300], n>9 in ListOfDigits(n)); # Muniru A Asiru, Feb 25 2019


CROSSREFS

Cf. A088924 (number of ndigit terms).
Cf. A087062 (lunar product), A087097 (lunar primes).
Cf. A007095 (numbers without digit 9), A102683 (number of digits 9 in n); fixed points > 8 of A068505.
Sequence in context: A037085 A088478 A088923 * A088479 A043525 A277596
Adjacent sequences: A011536 A011537 A011538 * A011540 A011541 A011542


KEYWORD

nonn,base,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



