A025623 -id:A025623 - cp's OEIS frontend

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

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

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

A108201 Numbers of the form (5^i)*(12^j), with i, j >= 0.

Original entry on oeis.org

1, 5, 12, 25, 60, 125, 144, 300, 625, 720, 1500, 1728, 3125, 3600, 7500, 8640, 15625, 18000, 20736, 37500, 43200, 78125, 90000, 103680, 187500, 216000, 248832, 390625, 450000, 518400, 937500, 1080000, 1244160, 1953125, 2250000, 2592000

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Jun 15 2005

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

Cf. A025622, A003595, A025623, A025624, A025625, A003598, A107466, A064476.

Take[Union[5^First[#] 12^Last[#]&/@Tuples[Range[0,20],2]],50] (* Harvey P. Dale, Mar 23 2012 *)

Sum_{n>=1} 1/a(n) = 15/11. - Amiram Eldar, Mar 29 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

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

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

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A108201 Numbers of the form (5^i)*(12^j), with i, j >= 0.

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

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

Views

Author

Keywords

Comments

Crossrefs