A025650 -id:A025650 - cp's OEIS frontend

A025617 Numbers of form 4^i*5^j, with i, j >= 0.

1, 4, 5, 16, 20, 25, 64, 80, 100, 125, 256, 320, 400, 500, 625, 1024, 1280, 1600, 2000, 2500, 3125, 4096, 5120, 6400, 8000, 10000, 12500, 15625, 16384, 20480, 25600, 32000, 40000, 50000, 62500, 65536, 78125, 81920, 102400, 128000, 160000, 200000, 250000

Offset: 1

David W. Wilson

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

Subsequence of A003592.

n = 10^5; Flatten[Table[4^i*5^j, {i, 0, Log[4, n]}, {j, 0, Log[5, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

Sum_{n>=1} 1/a(n) = (4*5)/((4-1)*(5-1)) = 5/3. - Amiram Eldar, Sep 24 2020
a(n) ~ exp(sqrt(2*log(4)*log(5)*n)) / sqrt(20). - Vaclav Kotesovec, Sep 24 2020
a(n) = 4^A025646(n) * 5^A025650(n). - R. J. Mathar, Jul 06 2025

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

A025674 Exponent of 8 (value of j) in n-th number of form 6^i*8^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. A025627, A025661, A244413.

Differs from A025650 at a(1881).

With[{max = 10^12}, SortBy[Flatten[Table[{i, j}, {i, 0, Log[6, max]}, {j, 0, Log[8, max/6^i]}], 1], 6^#[[1]] * 8^#[[2]] &][[;; , 2]]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A244413(A025627(n)/6^A025661(n)). - Amiram Eldar, Jul 09 2025

A025702 Index of 4^n within sequence of numbers of form 4^i*5^j.

Original entry on oeis.org

1, 2, 4, 7, 11, 16, 22, 29, 36, 44, 53, 63, 74, 86, 99, 112, 126, 141, 157, 174, 192, 211, 230, 250, 271, 293, 316, 340, 365, 390, 416, 443, 471, 500, 530, 561, 593, 625, 658, 692, 727, 763, 800, 838, 876, 915, 955, 996, 1038, 1081, 1125, 1169, 1214, 1260, 1307, 1355

Offset: 0

David W. Wilson

Positions of zeros in A025650. - R. J. Mathar, Jul 06 2025

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Differs from A025717 at a(65).

a(n)=my(N=1); n+1+sum(i=1, n, logint(N<<=2, 5)); \\ Charles R Greathouse IV, Jan 11 2018

first(n)=my(s, N=1/4); vector(n+1, i, s+=logint(N<<=2, 5)+1) \\ Charles R Greathouse IV, Jan 11 2018

Offset corrected by Charles R Greathouse IV, Jan 11 2018

cp's OEIS Frontend

A025617 Numbers of form 4^i*5^j, with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A025674 Exponent of 8 (value of j) in n-th number of form 6^i*8^j.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A025702 Index of 4^n within sequence of numbers of form 4^i*5^j.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

PARI

Extensions