A025619 -id:A025619 - cp's OEIS frontend

A107988 Numbers of the form (4^i)*(11^j), with i, j >= 0.

1, 4, 11, 16, 44, 64, 121, 176, 256, 484, 704, 1024, 1331, 1936, 2816, 4096, 5324, 7744, 11264, 14641, 16384, 21296, 30976, 45056, 58564, 65536, 85184, 123904, 161051, 180224, 234256, 262144, 340736, 495616, 644204, 720896, 937024, 1048576

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 12 2005

nonn

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

Subsequence of A003596.

Cf. A025617, A025618, A025619, A025620, A025621, A107462, A003597, A003598, A003599, A108090.

import Data.Set (singleton, deleteFindMin, insert)
a107988 n = a107988_list !! (n-1)
a107988_list = f $ singleton (1,0,0) where
   f s = y : f (insert (4 * 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[4^i*11^j, {i, 0, Log[4, n]}, {j, 0, Log[11, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

Sum_{n>=1} 1/a(n) = (4*11)/((4-1)*(11-1)) = 22/15. - Amiram Eldar, Sep 24 2020

a(n) ~ exp(sqrt(2*log(4)*log(11)*n)) / sqrt(44). - Vaclav Kotesovec, Sep 24 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

A107462 Numbers of the form (4^i)*(13^j), with i, j >= 0.

Original entry on oeis.org

1, 4, 13, 16, 52, 64, 169, 208, 256, 676, 832, 1024, 2197, 2704, 3328, 4096, 8788, 10816, 13312, 16384, 28561, 35152, 43264, 53248, 65536, 114244, 140608, 173056, 212992, 262144, 371293, 456976, 562432, 692224, 851968, 1048576, 1485172

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 09 2005

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

Subsequence of A107326.

Cf. A025617, A025618, A025619, A025620, A025621, A107364, A107466, A108056, A108090.

n = 10^6; Flatten[Table[4^i*13^j, {i, 0, Log[4, n]}, {j, 0, Log[13, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

Sum_{n>=1} 1/a(n) = (4*13)/((4-1)*(13-1)) = 13/9. - Amiram Eldar, Sep 24 2020

a(n) ~ exp(sqrt(2*log(4)*log(13)*n)) / sqrt(52). - Vaclav Kotesovec, Sep 24 2020

A025648 Exponent of 4 (value of i) in n-th number of form 4^i*7^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 2, 1, 4, 0, 3, 2, 5, 1, 4, 0, 3, 6, 2, 5, 1, 4, 7, 0, 3, 6, 2, 5, 8, 1, 4, 7, 0, 3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 10, 3, 6, 9, 2, 5, 8, 1, 11, 4, 7, 0, 10, 3, 6, 9, 2, 12, 5, 8, 1, 11, 4, 7, 0, 10, 3, 13, 6, 9, 2, 12, 5, 8, 1, 11, 4, 14, 7, 0, 10, 3, 13, 6, 9, 2, 12, 5, 15, 8, 1, 11, 4, 14, 7

Offset: 1

David W. Wilson

nonn

Cf. A025619.

A025666 Exponent of 7 (value of j) in n-th number of form 4^i*7^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

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

Cf. A025619, A025648.

N:= 10^10: # to consider all terms with 4^i*7^j<=N
S:= {seq(seq(4^i*7^j, j=0..floor(log[7](N/4^i))),i=0..floor(log[4](N)))}:
map(padic:-ordp, sort(convert(S,list)),7); # Robert Israel, Aug 11 2019

4^A025648(n)*7^a(n) = A025619(n). - Robert Israel, Aug 11 2019

cp's OEIS Frontend

A107988 Numbers of the form (4^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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A107462 Numbers of the form (4^i)*(13^j), with i, j >= 0.

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A025648 Exponent of 4 (value of i) in n-th number of form 4^i*7^j.

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A025666 Exponent of 7 (value of j) in n-th number of form 4^i*7^j.

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