A025672 -id:A025672 - cp's OEIS frontend

A025615 Numbers of form 3^i*8^j, with i, j >= 0.

1, 3, 8, 9, 24, 27, 64, 72, 81, 192, 216, 243, 512, 576, 648, 729, 1536, 1728, 1944, 2187, 4096, 4608, 5184, 5832, 6561, 12288, 13824, 15552, 17496, 19683, 32768, 36864, 41472, 46656, 52488, 59049, 98304, 110592, 124416, 139968, 157464, 177147, 262144

Offset: 1

David W. Wilson

Subset of A003586 3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0. - Daniel Forgues, Feb 24 2011

Indices for which a term is a power of 3 are in A025699 and a power of 8 are in A025728- Bernard Schott, Dec 27 2021

Georg Fischer, Table of n, a(n) for n = 1..300

Cf. A003586, A025699, A025728.

lim = 262144; Select[Sort[Flatten[Table[3^i 8^j, {i, 0, Log[3, lim]}, {j, 0, Log[8, lim]}]]], # <=lim &] (* T. D. Noe, Mar 01 2012 *)

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

Sum_{n>=1} 1/a(n) = 12/7. - Amiram Eldar, Feb 18 2021
From Bernard Schott, Dec 27 2021: (Start)
a(A025699(n)) = 3^(n-1).
a(A025728(n)) = 8^(n-1). (End)
a(n) = 3^A025643(n) * 8^A025672(n). - R. J. Mathar, Jul 06 2025

A216607 The sequence used to represent partition binary diagram as an array.

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

Offset: 1

Mircea Merca, Sep 10 2012

This sequence differs from A025672 first at index n=110.

Mircea Merca, Binary Diagrams for Storing Ascending Compositions, Comp. J., 2012.

Cf. A025672, A167268.

seq(floor((1/4)*ceil(sqrt(4*n))^2)-n,n=1..50)

A216607(n)=floor((1/4)*ceil(sqrt(4*n))^2)-n;

a(n) = floor((1/4)*ceiling(sqrt(4*n))^2) - n.
a(n^2) = a(n^2+n) = 0.
From Szymon Lukaszyk, Oct 27 2023: (Start)
a(n) = (-n) mod round(sqrt(n)).
a(n) = (A167268(n) - 2)/4. (End)

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]));

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

Original entry on oeis.org

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

cp's OEIS Frontend

A025615 Numbers of form 3^i*8^j, with i, j >= 0.

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A216607 The sequence used to represent partition binary diagram as an array.

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

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Maple

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

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