A056850 -id:A056850 - cp's OEIS frontend

A056576 Highest k with 2^k <= 3^n.

0, 1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 19, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103, 104, 106, 107

Offset: 0

Henry Bottomley, Jun 29 2000

nonn

			a(3)=4 because 3^3=27 and 2^4=16 is power of 2 immediately below 27.

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x+ 1 function, arXiv:1709.03385 [math.GM], 2017.

Cf. A000079 (powers of 2), A000244 (powers of 3), A020914, A022921.

Cf. A056850, A117630 (complement), A020857 (decimal expansion of log_2(3)), A076227, A100982.

a056576 = subtract 1 . a020914  -- Reinhard Zumkeller, May 17 2015

seq(ilog2(3^n), n= 0 .. 1000); # Robert Israel, Dec 11 2014

Table[Floor[Log[2, 3^n]], {n, 0, 69}] (* Robert G. Wilson v, Apr 06 2006 *)
Table[Floor[n*Log[2, 3]], {n, 0, 68}] (* L. Edson Jeffery, Dec 11 2014 *)

{a(n) = if( n<0, 0, logint(3^n, 2))}; /* Michael Somos, Dec 13 2014 */

def A056576(n): return (3**n).bit_length()-1 # Chai Wah Wu, Oct 09 2024

a(n) = floor(log_2(3^n)) = log_2(A000244(n)-A056576(n)) = a(n-1)+A022921(n-1).

a(n) = A020914(n) - 1. - L. Edson Jeffery, Dec 12 2014

A064024 a(n) = minimum value of abs(2^n - 3^k).

Original entry on oeis.org

0, 1, 1, 1, 7, 5, 17, 47, 13, 217, 295, 139, 1909, 1631, 3299, 13085, 6487, 46075, 84997, 7153, 517135, 502829, 588665, 3605639, 2428309, 9492289, 24062143, 5077565, 118985033, 149450423, 88519643, 985222181, 808182895, 1870418611

Offset: 0

Robert G. Wilson v, Sep 18 2001

nonn

			a(5) = 5 because |2^5 - 3^3| = 5.

Harry J. Smith, Table of n, a(n) for n = 0..500

Cf. A056850.

Do[ k = 0; While[ Abs[ 2^n - 3^k ] > Abs[ 2^n - 3^(k + 1) ], k++ ]; Print[ Abs[ 2^n - 3^k ]], {n, 0, 40} ]

{ p=t=1; for (n=0, 500, while ((a=abs(p - t)) > abs(p - 3*t), t*=3); write("b064024.txt", n, " ", a); p*=2 ) } \\ Harry J. Smith, Sep 06 2009

Name changed by Sean A. Irvine, Jun 08 2023

A014122 Numbers of form |2^i +- 3^j|.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 15, 17, 19, 23, 25, 26, 28, 29, 31, 33, 35, 37, 41, 43, 47, 49, 55, 59, 61, 63, 65, 67, 73, 77, 79, 80, 82, 83, 85, 89, 91, 97, 101, 113, 115, 119, 125, 127, 129, 131, 137, 139, 145, 155, 175, 179, 209, 211, 217, 227

Offset: 1

Richard C. Schroeppel

nonn

Based on checking i <= 100 and j <= 60.
Existing sequence correct for j <= 200000. - Sean A. Irvine, Oct 04 2018
2*k is a term iff 2*k = 3^j +- 1. - Sean A. Irvine, Oct 04 2018
Existing sequence correct for j <= 10^6. - David A. Corneth, Oct 04 2018
3*k is a term iff 3*k = 2^j +- 1. - Jon E. Schoenfield, Oct 04 2018

Cf. A014121, A056850.

Constraint on search moved from title to comments by Sean A. Irvine, Oct 04 2018

A086453 Least difference between 5^n and a power of 2.

Original entry on oeis.org

0, 1, 7, 3, 113, 971, 759, 12589, 128481, 144027, 1377017, 15273693, 24294831, 146961301, 1808548329, 3842160243, 15148937153, 213183639237, 583349245479, 1481300283709, 24998687462961, 86112795218187, 132385977330377

Offset: 0

Lekraj Beedassy, Sep 09 2003

nonn

Cf. A061785, A056850.

min(5^n-2^A061785(n), 2^(A061785(n)+1)-5^n), where A061785(n) is Beatty sequence for log[2](5). - Vladeta Jovovic, Sep 11 2003

More terms from Ray Chandler and John W. Layman, Sep 10 2003

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A056576 Highest k with 2^k <= 3^n.

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A064024 a(n) = minimum value of abs(2^n - 3^k).

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A014122 Numbers of form |2^i +- 3^j|.

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A086453 Least difference between 5^n and a power of 2.

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