A025615 -id:A025615 - cp's OEIS frontend

A025699 Index of 3^n within sequence of numbers of form 3^i*8^j (A025615).

1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, 42, 49, 56, 64, 72, 81, 90, 100, 111, 122, 134, 146, 159, 172, 186, 200, 215, 230, 246, 262, 279, 296, 314, 332, 351, 371, 391, 412, 433, 455, 477, 500, 523, 547, 571, 596, 621, 647, 673, 700, 727, 755, 784, 813, 843, 873, 904, 935

Offset: 1

David W. Wilson

nonn

Not same as A002620.
The first 19 positive terms are the same, then a(20) = 111 while A002620(21) = 110. - Bernard Schott, Dec 31 2021
Positions of zeros in A025672. - R. J. Mathar, Jul 06 2025

Cf. A002620, A003586, A025615, A025728 (similar for 8^n).

A025615(a(n)) = 3^(n-1). - Bernard Schott, Dec 27 2021

A025728 Index of 8^n within sequence of numbers of form 3^i*8^j (A025615).

Original entry on oeis.org

1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 110, 131, 154, 179, 206, 235, 266, 299, 334, 370, 408, 448, 490, 534, 580, 628, 678, 730, 783, 838, 895, 954, 1015, 1078, 1143, 1210, 1279, 1350, 1422, 1496, 1572, 1650, 1730, 1812, 1896, 1982, 2070, 2159, 2250, 2343, 2438

Offset: 1

David W. Wilson

nonn

Positions of zeros in A025643. - R. J. Mathar, Jul 06 2025

Cf. A025615, A025699 (similar for 3^n).

A025615(a(n)) = 8^(n-1). - Bernard Schott, Dec 27 2021

A025633 Numbers of form 8^i*9^j, with i, j >= 0.

Original entry on oeis.org

1, 8, 9, 64, 72, 81, 512, 576, 648, 729, 4096, 4608, 5184, 5832, 6561, 32768, 36864, 41472, 46656, 52488, 59049, 262144, 294912, 331776, 373248, 419904, 472392, 531441, 2097152, 2359296, 2654208, 2985984, 3359232, 3779136, 4251528, 4782969

Offset: 1

David W. Wilson

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

Subsequence of A025611 and A025615.

n = 10^6; Flatten[Table[8^i*9^j, {i, 0, Log[8, n]}, {j, 0, Log[9, n/8^i]}]] // Sort (* Amiram Eldar, Sep 25 2020 *)

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 9), N=9^n; while(N<=lim, listput(v, N); N<<=3)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Sum_{n>=1} 1/a(n) = (8*9)/((8-1)*(9-1)) = 9/7. - Amiram Eldar, Sep 25 2020
a(n) ~ exp(sqrt(2*log(8)*log(9)*n)) / sqrt(72). - Vaclav Kotesovec, Sep 25 2020
a(n) = 8^A025676(n) * 9^A025682(n). - R. J. Mathar, Jul 06 2025

A025672 Exponent of 8 (value of j) in n-th number of form 3^i*8^j.

Original entry on oeis.org

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

Offset: 1

David W. Wilson

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..10000
Sean A. Irvine, Table of n, a(n) for n = 1..981730 [a large file]
OEIS server, Scatterplot of n, a(n) with n=1..10^6.

A025672(n)=valuation(A025615(n),8) \\ M. F. Hasler, Feb 20 2012

for(n=1,1e9,n==8^valuation(n,8)*3^valuation(n,3)&&print1(valuation(n,8),", ")) \\ M. F. Hasler, Feb 20 2012

a(n) = valuation(A025615(n),8) = valuation(A025615(n),2)/3 = A007814(A025615(n))/3. - M. F. Hasler, Feb 20 2012

Incorrect formula deleted by Sean A. Irvine, Feb 20 2012

A025643 Exponent of 3 (value of i) in n-th number of form 3^i*8^j.

Original entry on oeis.org

0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 5, 0, 2, 4, 6, 1, 3, 5, 7, 0, 2, 4, 6, 8, 1, 3, 5, 7, 9, 0, 2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 11, 0, 2, 4, 6, 8, 10, 12, 1, 3, 5, 7, 9, 11, 13, 0, 2, 4, 6, 8, 10, 12, 14, 1, 3, 5, 7, 9, 11, 13, 15, 0, 2, 4, 6, 8, 10, 12, 14, 16, 1, 3, 5, 7, 9, 11, 13, 15, 17, 0, 2, 4, 6, 8, 10

Offset: 1

David W. Wilson

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A025615, A025672.

N:= 10^40: # include entries for all 3^i*8^j <= N
map(t -> t[1],sort([seq(seq([i,j],j=0..floor(log[8](N/3^i))),i=0..floor(log[3](N)))],(s,t) -> 3^s[1]*8^s[2]<=3^t[1]*8^t[2]));

cp's OEIS Frontend

A025699 Index of 3^n within sequence of numbers of form 3^i*8^j (A025615).

Views

Author

Keywords

Comments

Crossrefs

Formula

A025728 Index of 8^n within sequence of numbers of form 3^i*8^j (A025615).

Views

Author

Keywords

Comments

Crossrefs

Formula

A025633 Numbers of form 8^i*9^j, with i, j >= 0.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A025672 Exponent of 8 (value of j) in n-th number of form 3^i*8^j.

Views

Author

Keywords

Links

Programs

PARI

PARI

Formula

Extensions

A025643 Exponent of 3 (value of i) in n-th number of form 3^i*8^j.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple