A025686 -id:A025686 - 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

A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^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

Cf. A025621. Differs from A025641 at a(114). A025686 is exponent of 10.

A025657 Exponent of 6 (value of j) in n-th number of form 3^i*6^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

Differs from A025686 at a(114). A025641 is the exponent of 3 (value of i).

Cf. A025614, A025641 (exponent of 3).

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

A025705 Index of 4^n within sequence of numbers of form 4^i*10^j.

Original entry on oeis.org

1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 40, 47, 55, 63, 72, 82, 92, 103, 114, 126, 139, 152, 166, 180, 195, 211, 227, 244, 261, 279, 298, 317, 337, 357, 378, 400, 422, 445, 468, 492, 517, 542, 568, 594, 621, 649, 677, 706, 735, 765, 796, 827, 859, 891, 924, 958, 992, 1027

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025686. - R. J. Mathar, Jul 06 2025

cp's OEIS Frontend

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

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A025649 Exponent of 4 (value of i) in n-th number of form 4^i*10^j.

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A025657 Exponent of 6 (value of j) in n-th number of form 3^i*6^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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A025705 Index of 4^n within sequence of numbers of form 4^i*10^j.

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