A025628 -id:A025628 - cp's OEIS frontend

A025629 Numbers of form 6^i*10^j with i, j >= 0.

1, 6, 10, 36, 60, 100, 216, 360, 600, 1000, 1296, 2160, 3600, 6000, 7776, 10000, 12960, 21600, 36000, 46656, 60000, 77760, 100000, 129600, 216000, 279936, 360000, 466560, 600000, 777600, 1000000, 1296000, 1679616, 2160000, 2799360, 3600000, 4665600

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A025610, A025618, A025622, A025626, A025627, A025628.

Cf. A025612, A025616, A025621, A025625, A025632, A025634.

n = 10^6; Flatten[Table[6^i*10^j, {i, 0, Log[6, n]}, {j, 0, Log10[n/6^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N*=6)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Sum_{n>=1} 1/a(n) = (6*10)/((6-1)*(10-1)) = 4/3. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(6)*log(10)*n)) / sqrt(60). - Vaclav Kotesovec, Sep 26 2020
a(n) = 6^A025663(n) * 10^A025688(n). - R. J. Mathar, Jul 06 2025

A108698 Numbers of the form (6^i)*(11^j), with i, j >= 0.

Original entry on oeis.org

1, 6, 11, 36, 66, 121, 216, 396, 726, 1296, 1331, 2376, 4356, 7776, 7986, 14256, 14641, 26136, 46656, 47916, 85536, 87846, 156816, 161051, 279936, 287496, 513216, 527076, 940896, 966306, 1679616, 1724976, 1771561, 3079296, 3162456

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 19 2005

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A025626, A025627, A025628, A025629, A064476, A107710, A003596, A003597, A107988, A003598, A108687, A003599, A107788, A108090.

import Data.Set (singleton, deleteFindMin, insert)
a108698 n = a108698_list !! (n-1)
a108698_list = f $ singleton (1,0,0) where
   f s = y : f (insert (6 * y, i + 1, j) $ insert (11 * y, i, j + 1) s')
         where ((y, i, j), s') = deleteFindMin s
-- Reinhard Zumkeller, May 15 2015

n = 10^6; Flatten[Table[6^i*11^j, {i, 0, Log[6, n]}, {j, 0, Log[11, n/6^i]}]] // Sort (* Amiram Eldar, Oct 07 2020 *)

Sum_{n>=1} 1/a(n) = (6*11)/((6-1)*(11-1)) = 33/25. - Amiram Eldar, Oct 07 2020

a(n) ~ exp(sqrt(2*log(6)*log(11)*n)) / sqrt(66). - Vaclav Kotesovec, Oct 07 2020

A025626 Numbers of form 6^i*7^j, with i, j >= 0.

Original entry on oeis.org

1, 6, 7, 36, 42, 49, 216, 252, 294, 343, 1296, 1512, 1764, 2058, 2401, 7776, 9072, 10584, 12348, 14406, 16807, 46656, 54432, 63504, 74088, 86436, 100842, 117649, 279936, 326592, 381024, 444528, 518616, 605052, 705894, 823543, 1679616, 1959552

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A025610, A025622, A025627, A025628, A025629.

Cf. A025619, A025631, A025632, A003591, A003594, A003595, A036566.

n = 10^6; Flatten[Table[6^i*7^j, {i, 0, Log[6, n]}, {j, 0, Log[7, n/6^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (6*7)/((6-1)*(7-1)) = 7/5. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(6)*log(7)*n)) / sqrt(42). - Vaclav Kotesovec, Sep 25 2020
a(n) = 6^A025660(n) * 7^A025668(n). - R. J. Mathar, Jul 06 2025

A107710 Numbers of the form (6^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 6, 13, 36, 78, 169, 216, 468, 1014, 1296, 2197, 2808, 6084, 7776, 13182, 16848, 28561, 36504, 46656, 79092, 101088, 171366, 219024, 279936, 371293, 474552, 606528, 1028196, 1314144, 1679616, 2227758, 2847312, 3639168, 4826809, 6169176

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 10 2005

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A025626, A025627, A025628, A025629, A064476, A107326, A107364, A107462, A107466, A108056, A108090.

n = 10^6; Flatten[Table[6^i*13^j, {i, 0, Log[6, n]}, {j, 0, Log[13, n/6^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (6*13)/((6-1)*(13-1)) = 13/10. - Amiram Eldar, Sep 25 2020

a(n) ~ exp(sqrt(2*log(6)*log(13)*n)) / sqrt(78). - Vaclav Kotesovec, Sep 25 2020

A025614 Numbers of form 3^i*6^j, with i, j >= 0.

Original entry on oeis.org

1, 3, 6, 9, 18, 27, 36, 54, 81, 108, 162, 216, 243, 324, 486, 648, 729, 972, 1296, 1458, 1944, 2187, 2916, 3888, 4374, 5832, 6561, 7776, 8748, 11664, 13122, 17496, 19683, 23328, 26244, 34992, 39366, 46656, 52488, 59049, 69984, 78732, 104976, 118098

Offset: 1

David W. Wilson

Amiram Eldar, Table of n, a(n) for n = 1..10000

A025628 is a subsequence.
Cf. A003586, A003593, A003594, A003597, A107364.
Cf. A025610, A025618, A025622, A025626, A025627.

n = 10^6; Flatten[Table[3^i*6^j, {i, 0, Log[3, n]}, {j, 0, Log[6, n/3^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

Sum_{n>=1} 1/a(n) = (3*6)/((3-1)*(6-1)) = 9/5. - Amiram Eldar, Sep 26 2020
a(n) ~ exp(sqrt(2*log(3)*log(6)*n)) / sqrt(18). - Vaclav Kotesovec, Sep 26 2020
a(n) = 3^A025641(n) *6^A025657(n). - R. J. Mathar, Jul 06 2025

A025662 Exponent of 6 (value of i) in n-th number of form 6^i*9^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 6, 0, 5, 4, 3, 2, 7, 1, 6, 0, 5, 4, 3, 8, 2, 7, 1, 6, 0, 5, 4, 9, 3, 8, 2, 7, 1, 6, 0, 5, 10, 4, 9, 3, 8, 2, 7, 1, 6, 11, 0, 5, 10, 4, 9, 3, 8, 2, 7, 12, 1, 6, 11, 0, 5, 10, 4, 9, 3, 8, 13, 2, 7, 12, 1, 6, 11, 0, 5, 10, 4, 9, 14, 3, 8, 13, 2, 7, 12, 1, 6

Offset: 1

David W. Wilson

nonn

Cf. A025628.

A025680 Exponent of 9 (value of j) in n-th number of form 6^i*9^j.

Original entry on oeis.org

0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 5, 1, 2, 3, 4, 0, 5, 1, 6, 2, 3, 4, 0, 5, 1, 6, 2, 7, 3, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 0, 5, 1, 6, 2, 7, 3, 8, 4, 0, 9, 5, 1, 6, 2, 7, 3, 8, 4, 0, 9, 5, 1, 10, 6, 2, 7, 3, 8, 4, 0, 9, 5, 1, 10, 6, 2, 11, 7, 3, 8, 4, 0, 9, 5, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4

Offset: 1

David W. Wilson

nonn

Cf. A025628.

A025718 Index of 6^n within sequence of numbers of form 6^i*9^j.

Original entry on oeis.org

1, 2, 4, 7, 11, 16, 21, 27, 34, 42, 51, 60, 70, 81, 93, 106, 120, 134, 149, 165, 182, 200, 218, 237, 257, 278, 300, 323, 346, 370, 395, 421, 448, 475, 503, 532, 562, 593, 624, 656, 689, 723, 758, 794, 830, 867, 905, 944, 984, 1024, 1065, 1107, 1150, 1194, 1239, 1284

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025680. - R. J. Mathar, Jul 06 2025

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A025628.

with(priqueue):
initialize(PQ):
insert([-1,0,0],PQ):
count:= 0: R:= NULL:
for i from 1 while count < 100 do
  v:= extract(PQ);
if v[3] = 0 then R:= R,i; count:= count+1; insert([v[1]*6,v[2]+1,0],PQ);
insert([v[1]*9, v[2], v[3]+1],PQ)
od:
R; # Robert Israel, Jan 21 2024

cp's OEIS Frontend

A025629 Numbers of form 6^i*10^j with i, j >= 0.

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A108698 Numbers of the form (6^i)*(11^j), with i, j >= 0.

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A025626 Numbers of form 6^i*7^j, with i, j >= 0.

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A107710 Numbers of the form (6^i)*(13^j), with i, j >= 0.

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A025614 Numbers of form 3^i*6^j, with i, j >= 0.

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A025662 Exponent of 6 (value of i) in n-th number of form 6^i*9^j.

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A025680 Exponent of 9 (value of j) in n-th number of form 6^i*9^j.

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A025718 Index of 6^n within sequence of numbers of form 6^i*9^j.

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Maple