A025617 -id:A025617 - 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

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

A025646 Exponent of 4 (value of i) in n-th number of form 4^i*5^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, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 8, 0, 7, 6, 5, 4, 3, 2, 9, 1, 8, 0, 7, 6, 5, 4, 3, 10, 2, 9, 1, 8, 0, 7, 6, 5, 4, 11, 3, 10, 2, 9, 1, 8, 0, 7, 6, 5, 12, 4, 11, 3, 10, 2, 9, 1, 8, 0, 7, 6, 13, 5, 12, 4, 11, 3, 10, 2, 9, 1, 8, 0, 7, 14, 6, 13

Offset: 1

David W. Wilson

nonn

Cf. A025617, A025650, A235127.

Differs from A025661 at a(1881).

With[{nn=15},IntegerExponent[#,4]&/@Union[Flatten[Table[4^x 5^y,{x,0,nn},{y,0,nn}]]]] (* Harvey P. Dale, May 10 2019 *)
With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*5^j, {i, 0, Log[4, max]}, {j, 0, Log[5, max/4^i]}]]], 4]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A235127(A025617(n)). - Amiram Eldar, Jul 09 2025

A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^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, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 7, 1, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 6, 0, 7, 1, 8, 2, 9, 3, 10, 4, 11, 5, 12, 6, 0, 7, 1, 8, 2, 9

Offset: 1

David W. Wilson

nonn

Cf. A025617, A025646, A112765.

Differs from A025674 at a(1881).

With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*5^j, {i, 0, Log[4, max]}, {j, 0, Log[5, max/4^i]}]]], 5]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A112765(A025617(n)). - Amiram Eldar, Jul 09 2025

cp's OEIS Frontend

A107988 Numbers of the form (4^i)*(11^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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A025646 Exponent of 4 (value of i) in n-th number of form 4^i*5^j.

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A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^j.

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