A025649 -id:A025649 - cp's OEIS frontend

A025621 Numbers of form 4^i*10^j, with i, j >= 0.

1, 4, 10, 16, 40, 64, 100, 160, 256, 400, 640, 1000, 1024, 1600, 2560, 4000, 4096, 6400, 10000, 10240, 16000, 16384, 25600, 40000, 40960, 64000, 65536, 100000, 102400, 160000, 163840, 256000, 262144, 400000, 409600, 640000, 655360, 1000000, 1024000

Offset: 1

David W. Wilson

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Subsequence of A025612.

n = 10^6; Flatten[Table[4^i*10^j, {i, 0, Log[4, n]}, {j, 0, Log10[n/4^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 10), N=10^n; while(N<=lim, listput(v, N); N<<=2)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Sum_{n>=1} 1/a(n) = (4*10)/((4-1)*(10-1)) = 40/27. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(4)*log(10)*n)) / sqrt(40). - Vaclav Kotesovec, Sep 25 2020
a(n) = 4^A025649(n) * 10^A025686(n). - R. J. Mathar, Jul 06 2025

A025641 Exponent of 3 (value of i) in n-th number of form 3^i*6^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, 0, 5, 2, 7, 4, 1, 6, 3, 8, 0, 5, 2, 7, 4, 9, 1, 6, 3, 8, 0, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 0, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 0, 5, 10, 2, 7, 12, 4, 9, 14, 1, 6, 11, 3, 8, 13, 0, 5, 10, 15, 2, 7, 12, 4, 9, 14, 1, 6, 11, 16, 3, 8, 13, 0, 5, 10

Offset: 1

David W. Wilson

nonn

Also known as (exponent of 3 in n-th number of the form 3^i * 6^j) - (exponent of 2 in n-th number of the form 3^i * 6^j). - David A. Corneth, Jan 12 2021

			a(5) = 1 as the 5th number of the form 3^i * 6^j is 18 = 3^1 * 6^1 which has exponent of 3 equal to 1. - _David A. Corneth_, Jan 12 2021

David A. Corneth, Table of n, a(n) for n = 1..10000

Differs from A025649 at a(114). A025657 is exponent of 6.

Cf. A025614.

SortBy[Join @@ Table[{i, 3^i*6^j}, {i, 0, Log[3, #]}, {j, 0, Log[6, #/3^i]}], Last] &[10^8][[All, 1]] (* Michael De Vlieger, Jan 12 2021, after Amiram Eldar at A025614 *)

A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Cf. A025621. Differs from A025657 at a(114). A025649 is the exponent of 4.

A025742 a(n) is the index of 10^n within sequence of numbers of form 4^i*10^j.

Original entry on oeis.org

1, 3, 7, 12, 19, 28, 38, 50, 64, 79, 96, 115, 135, 157, 181, 206, 233, 262, 292, 324, 358, 393, 430, 469, 509, 551, 595, 640, 687, 736, 786, 838, 892, 947, 1004, 1063, 1123, 1185, 1249, 1314, 1381, 1450, 1520, 1592, 1666, 1741, 1818, 1897, 1977, 2059, 2143, 2228

Offset: 0

David W. Wilson

Indices m for which A025649(m) is 0. - Michel Marcus, Jan 10 2018

			The index of 10^0 in A025621 is 1, so a(0)=1.
The index of 10^1 in A025621 is 3, so a(1)=3.
The index of 10^2 in A025621 is 7, so a(2)=7.

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

Cf. A025621, A025649, A025686.

a(n)=my(N=1); n+1+sum(i=1,n, logint(N*=10,4)); \\ Charles R Greathouse IV, Jan 10 2018

first(n)=my(s,N=1/10); vector(n+1,i, s+=logint(N*=10,4)+1) \\ Charles R Greathouse IV, Jan 10 2018

Offset changed by Michel Marcus, Jan 10 2018

cp's OEIS Frontend

A025621 Numbers of form 4^i*10^j, with i, j >= 0.

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A025641 Exponent of 3 (value of i) in n-th number of form 3^i*6^j.

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A025686 Exponent of 10 (value of j) in n-th number of form 4^i*10^j.

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A025742 a(n) is the index of 10^n within sequence of numbers of form 4^i*10^j.

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