A025653 -id:A025653 - cp's OEIS frontend

A025623 Numbers of form 5^i*8^j, with i, j >= 0.

1, 5, 8, 25, 40, 64, 125, 200, 320, 512, 625, 1000, 1600, 2560, 3125, 4096, 5000, 8000, 12800, 15625, 20480, 25000, 32768, 40000, 64000, 78125, 102400, 125000, 163840, 200000, 262144, 320000, 390625, 512000, 625000, 819200, 1000000, 1310720

Offset: 1

David W. Wilson

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

Subsequence of A003592.

n = 10^6; Flatten[Table[5^i*8^j, {i, 0, Log[5, n]}, {j, 0, Log[8, n/5^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

Sum_{n>=1} 1/a(n) = (5*8)/((5-1)*(8-1)) = 10/7. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(5)*log(8)*n)) / sqrt(40). - Vaclav Kotesovec, Sep 25 2020
a(n) = 5^A025653(n) * 8^A025673(n). - R. J. Mathar, Jul 06 2025

A025647 Exponent of 4 (value of i) in n-th number of form 4^i*6^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025618, A025658, A235127.

Differs from A025653 at a(2805).

With[{max = 10^10}, SortBy[Flatten[Table[{i, j}, {i, 0, Log[4, max]}, {j, 0, Log[6, max/4^i]}], 1], 4^#[[1]] * 6^#[[2]] &][[;; , 1]]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A235127(A025618(n)/6^A025658(n)). - Amiram Eldar, Jul 09 2025

A025673 Exponent of 8 (value of j) in n-th number of form 5^i*8^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025623, A025653, A244413.

Differs from A025658 at a(2805).

Take[Sort[Flatten[Table[{5^i 8^j,j},{i,0,20},{j,0,20}],1]][[;;,2]],120] (* Harvey P. Dale, Nov 10 2024 *)
With[{max = 10^11}, IntegerExponent[Sort[Flatten[Table[5^i*8^j, {i, 0, Log[5, max]}, {j, 0, Log[8, max/5^i]}]]], 8]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A244413(A025623(n)). - Amiram Eldar, Jul 09 2025

A025683 Exponent of 9 (value of i) in n-th number of form 9^i*10^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, 0, 8, 7, 6, 5, 4, 3, 2, 1, 0, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3

Offset: 1

David W. Wilson

nonn

Cf. A025653. Differs from A025581 at a(253).

Table[Range[n,0,-1],{n,0,15}]//Flatten (* Harvey P. Dale, Jan 20 2022 *)

A025729 Index of 8^n within sequence of numbers of form 5^i*8^j.

Original entry on oeis.org

1, 3, 6, 10, 16, 23, 31, 41, 52, 64, 77, 92, 108, 125, 144, 164, 185, 207, 231, 256, 282, 310, 339, 369, 401, 434, 468, 503, 540, 578, 617, 658, 700, 743, 787, 833, 880, 928, 978, 1029, 1081, 1134, 1189, 1245, 1302, 1361, 1421, 1482, 1545, 1609, 1674, 1740, 1808

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025653. - R. J. Mathar, Jul 06 2025

Cf. A001018, A025623.

Differs from A025714 at a(65).

cp's OEIS Frontend

A025623 Numbers of form 5^i*8^j, with i, j >= 0.

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A025647 Exponent of 4 (value of i) in n-th number of form 4^i*6^j.

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A025673 Exponent of 8 (value of j) in n-th number of form 5^i*8^j.

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A025683 Exponent of 9 (value of i) in n-th number of form 9^i*10^j.

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A025729 Index of 8^n within sequence of numbers of form 5^i*8^j.

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