A329193 -id:A329193 - cp's OEIS frontend

A329194 a(n) = floor(log_3(n^2)) = floor(2 log_3(n)).

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

Offset: 1

M. F. Hasler, Nov 07 2019

nonn

Cf. A000290 (n^2), A062153 (log_3), A329202 (log_2(n^2)), A329193 (log_2(n^3)).

Table[Floor[Log[3,n^2]],{n,120}] (* Harvey P. Dale, May 04 2025 *)

apply( A329194(n)=logint(n^2,3), [1..99])

2*A062153(n) <= a(n) = floor(log_3(n^2)) = A062153(A000290(n)).

This A329194 = A062153 o A000290.

A338433 Values of n for which A070939(n^3) differs from A004221(n).

Original entry on oeis.org

1, 20, 40, 80, 101, 126, 127, 159, 160, 161, 200, 201, 202, 203, 252, 253, 254, 255, 317, 318, 319, 320, 321, 322, 399, 400, 401, 402, 403, 404, 405, 406, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645

Offset: 1

Jeremy Gardiner, Oct 27 2020

nonn

Sequence gives the values of n for which the length of the binary representation of n^3 differs from ceiling(10*log_10(n)) rounded up.

The largest number not in the sequence is 158489319246111348520210137339 = floor(10^29.2). - Robert Israel, Oct 27 2020

Jeremy Gardiner, Table of n, a(n) for n = 1..1083
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A004221, A070939, A111393, A329193.

filter:= n -> evalb(ilog2(n^3)+1 <> ceil(10*log[10](n))):
select(filter, [$1..1000]); # Robert Israel, Oct 27 2020

Select[Range[1000], IntegerLength[#^3, 2] != Ceiling[10*Log10[#]] &] (* Amiram Eldar, Oct 27 2020 *)

A225668 a(n) = floor(4*log_2(n)).

Original entry on oeis.org

0, 4, 6, 8, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24

Offset: 1

Jonathan Vos Post, May 11 2013

Arises in analysis of "when to clean your room".

			a(3) = floor(4*log_2(3)) = floor(6.33985000) = 6.
a(8) = floor(4*log_2(8)) = floor(4*3) = 12.

Kimball Martin and Krishnan Shankar, How often should you clean your room?, arXiv:1305.1984 [math.CO], 2013-2014.

Cf. A000583 (n^4), A000523 (floor log_2), A004257 (round log_2), A029837 (ceiling log_2).

Cf. A329202 (log_2(n^2)), A329193 (log_2(n^3)).

A225668 := proc(n)
    4*log[2](n) ;
    floor(%) ;
end proc: # R. J. Mathar, May 12 2013

Table[Floor[4*Log[2, n]], {n, 1, 64}] (* Jean-François Alcover, Nov 30 2017 *)

a(n) = 4*log(n)\log(2); \\ Michel Marcus, Nov 30 2017

apply( A225668(n)=exponent(n^4), [1..99]) \\ M. F. Hasler, Nov 07 2019

a(n) = floor(4*log(n)/log(2)).

a(n) = floor(log_2(n^4)) = A000523(A000583(n)), i.e., this A225668 = A000523 o A000583. - M. F. Hasler, Nov 07 2019

Better definition from M. F. Hasler, Nov 07 2019

A329195 a(n) = floor(log_5(n^2)) = floor(2 log_5(n)).

Original entry on oeis.org

0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

M. F. Hasler, Nov 07 2019

nonn

Cf. A000290 (n^2), A062153 (log_3), A329202 (log_2(n^2)), A329193 (log_2(n^3)), A329194 (log_3(n^2)).

Table[Floor[2Log[5,n]],{n,100}] (* Harvey P. Dale, Dec 14 2021 *)

apply( A329195(n)=logint(n^2,5), [1..99])

cp's OEIS Frontend

A329194 a(n) = floor(log_3(n^2)) = floor(2 log_3(n)).

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A338433 Values of n for which A070939(n^3) differs from A004221(n).

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A225668 a(n) = floor(4*log_2(n)).

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A329195 a(n) = floor(log_5(n^2)) = floor(2 log_5(n)).

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