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A108687
Numbers of the form (9^i)*(11^j), with i, j >= 0.
12
1, 9, 11, 81, 99, 121, 729, 891, 1089, 1331, 6561, 8019, 9801, 11979, 14641, 59049, 72171, 88209, 107811, 131769, 161051, 531441, 649539, 793881, 970299, 1185921, 1449459, 1771561, 4782969, 5845851, 7144929, 8732691, 10673289, 13045131
OFFSET
1,2
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = (9*11)/((9-1)*(11-1)) = 99/80. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(9)*log(11)*n)) / sqrt(99). - Vaclav Kotesovec, Sep 24 2020
MATHEMATICA
f[upto_]:=With[{max9=Floor[Log[9, upto]], max11=Floor[Log[11, upto]]}, Select[Union[Times@@{9^First[#], 11^Last[#]}&/@Tuples[{Range[0, max9], Range[0, max11]}]], #<=upto&]]; f[14000000] (* Harvey P. Dale, Mar 11 2011 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a108687 n = a108687_list !! (n-1)
a108687_list = f $ singleton (1, 0, 0) where
f s = y : f (insert (9 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Douglas Winston (douglas.winston(AT)srupc.com), Jun 17 2005
STATUS
approved