A107788
Numbers of the form (8^i)*(11^j), with i, j >= 0.
Original entry on oeis.org
1, 8, 11, 64, 88, 121, 512, 704, 968, 1331, 4096, 5632, 7744, 10648, 14641, 32768, 45056, 61952, 85184, 117128, 161051, 262144, 360448, 495616, 681472, 937024, 1288408, 1771561, 2097152, 2883584, 3964928, 5451776, 7496192, 10307264
Offset: 1
Douglas Winston (douglas.winston(AT)srupc.com), Jun 14 2005
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import Data.Set (singleton, deleteFindMin, insert)
a107788 n = a107788_list !! (n-1)
a107788_list = f $ singleton (1,0,0) where
f s = y : f (insert (8 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
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Take[Union[8^First[#]*11^Last[#]&/@Tuples[Range[0,20],2]],40] (* Harvey P. Dale, Jan 17 2015 *)
n = 10^6; Flatten[Table[8^i*11^j, {i, 0, Log[8, n]}, {j, 0, Log[11, n/8^i]}]] // Sort (* Amiram Eldar, Oct 07 2020 *)
A108687
Numbers of the form (9^i)*(11^j), with i, j >= 0.
Original entry on oeis.org
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
Douglas Winston (douglas.winston(AT)srupc.com), Jun 17 2005
-
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
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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 *)
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from sympy import integer_log
def A108687(n):
def bisection(f,kmin=0,kmax=1):
while f(kmax) > kmax: kmax <<= 1
kmin = kmax >> 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def f(x): return n+x-sum(integer_log(x//11**i,9)[0]+1 for i in range(integer_log(x,11)[0]+1))
return bisection(f,n,n) # Chai Wah Wu, Mar 25 2025
A108761
Numbers of the form (10^i)*(13^j), with i, j >= 0.
Original entry on oeis.org
1, 10, 13, 100, 130, 169, 1000, 1300, 1690, 2197, 10000, 13000, 16900, 21970, 28561, 100000, 130000, 169000, 219700, 285610, 371293, 1000000, 1300000, 1690000, 2197000, 2856100, 3712930, 4826809, 10000000, 13000000, 16900000
Offset: 1
Douglas Winston (douglas.winston(AT)srupc.com), Jun 24 2005
-
import Data.Set (singleton, deleteFindMin, insert)
a108761 n = a108761_list !! (n-1)
a108761_list = f $ singleton (1,0,0) where
f s = y : f (insert (10 * y, i + 1, j) $ insert (13 * y, i, j + 1) s')
where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015
-
n = 10^7; Flatten[Table[10^i*13^j, {i, 0, Log10[n]}, {j, 0, Log[13, n/10^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)
A108748
Numbers of the form (9^i)*(13^j), with i, j >= 0.
Original entry on oeis.org
1, 9, 13, 81, 117, 169, 729, 1053, 1521, 2197, 6561, 9477, 13689, 19773, 28561, 59049, 85293, 123201, 177957, 257049, 371293, 531441, 767637, 1108809, 1601613, 2313441, 3341637, 4782969, 4826809, 6908733, 9979281, 14414517, 20820969
Offset: 1
Douglas Winston (douglas.winston(AT)srupc.com), Jun 23 2005
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n = 10^6; Flatten[Table[9^i*13^j, {i, 0, Log[9, n]}, {j, 0, Log[13, n/9^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)
A108771
Numbers of the form (12^i)*(13^j), with i, j >= 0.
Original entry on oeis.org
1, 12, 13, 144, 156, 169, 1728, 1872, 2028, 2197, 20736, 22464, 24336, 26364, 28561, 248832, 269568, 292032, 316368, 342732, 371293, 2985984, 3234816, 3504384, 3796416, 4112784, 4455516, 4826809, 35831808, 38817792, 42052608, 45556992
Offset: 1
Douglas Winston (douglas.winston(AT)srupc.com), Jun 25 2005
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N:= 10^8: # to get all terms <= N
sort([seq(seq(12^i*13^j, j = 0 .. floor(log[13](N/12^i))), i=0..floor(log[12](N)))]); # Robert Israel, Jun 16 2019
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With[{max = 5*10^7}, Flatten[Table[12^i*13^j, {i, 0, Log[12, max]}, {j, 0, Log[13, max/12^i]}]] // Sort] (* Amiram Eldar, Mar 29 2025 *)
Showing 1-5 of 5 results.