A025673 -id:A025673 - 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

A025653 Exponent of 5 (value of i) in n-th number of form 5^i*8^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. A025623, A025673, A112765.

Differs from A025647 at a(2805).

With[{max = 10^11}, IntegerExponent[Sort[Flatten[Table[5^i*8^j, {i, 0, Log[5, max]}, {j, 0, Log[8, max/5^i]}]]], 5]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A112765(A025623(n)). - Amiram Eldar, Jul 09 2025

A025658 Exponent of 6 (value of j) in n-th number of form 4^i*6^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. A025618, A025647, A122841.

Differs from A025673 at a(2805).

With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*6^j, {i, 0, Log[4, max]}, {j, 0, Log[6, max/4^i]}]]], 6]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A122841(A025618(n)). - Amiram Eldar, Jul 09 2025

A025709 Index of 5^n within sequence of numbers of form 5^i*8^j.

Original entry on oeis.org

1, 2, 4, 7, 11, 15, 20, 26, 33, 40, 48, 57, 67, 78, 89, 101, 114, 128, 142, 157, 173, 190, 208, 226, 245, 265, 286, 307, 329, 352, 376, 400, 425, 451, 478, 506, 534, 563, 593, 624, 655, 687, 720, 754, 789, 824, 860, 897, 935, 973, 1012, 1052, 1093, 1135, 1177, 1220

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025673. - R. J. Mathar, Jul 06 2025

Cf. A025623. Differs from A025703 at a(84).

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=5, 8)); \\ Charles R Greathouse IV, Jan 16 2018

first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 8)+1) \\ Charles R Greathouse IV, Jan 16 2018

cp's OEIS Frontend

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A025653 Exponent of 5 (value of i) in n-th number of form 5^i*8^j.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A025658 Exponent of 6 (value of j) in n-th number of form 4^i*6^j.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A025709 Index of 5^n within sequence of numbers of form 5^i*8^j.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

PARI