A025646 -id:A025646 - 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

A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^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. A025617, A025646, A112765.

Differs from A025674 at a(1881).

With[{max = 10^10}, IntegerExponent[Sort[Flatten[Table[4^i*5^j, {i, 0, Log[4, max]}, {j, 0, Log[5, max/4^i]}]]], 5]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A112765(A025617(n)). - Amiram Eldar, Jul 09 2025

A025661 Exponent of 6 (value of i) in n-th number of form 6^i*8^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. A025627, A025674, A122841.

Differs from A025646 at a(1881).

With[{max = 10^12}, IntegerExponent[Sort[Flatten[Table[6^i*8^j, {i, 0, Log[6, max]}, {j, 0, Log[8, max/6^i]}]]], 6]] (* Amiram Eldar, Jul 09 2025 *)

a(n) = A122841(A025627(n)). - Amiram Eldar, Jul 09 2025

A025706 Index of 5^n within sequence of numbers of form 4^i*5^j.

Original entry on oeis.org

1, 3, 6, 10, 15, 21, 28, 37, 47, 58, 70, 83, 97, 113, 130, 148, 167, 187, 208, 231, 255, 280, 306, 333, 361, 391, 422, 454, 487, 521, 556, 592, 630, 669, 709, 750, 792, 835, 880, 926, 973, 1021, 1070, 1120, 1172, 1225, 1279, 1334, 1390, 1447, 1506, 1566, 1627, 1689

Offset: 0

David W. Wilson

Positions of zeros in A025646. - R. J. Mathar, Jul 06 2025

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

Cf. A025646. Differs from A025730 at a(56).

a(n)=my(N=1); n+1+sum(i=1, n, logint(N*=5, 4)); \\ Charles R Greathouse IV, Jan 11 2018

first(n)=my(s, N=1/5); vector(n+1, i, s+=logint(N*=5, 4)+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.

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A025650 Exponent of 5 (value of j) in n-th number of form 4^i*5^j.

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

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A025706 Index of 5^n within sequence of numbers of form 4^i*5^j.

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