A152747 -id:A152747 - cp's OEIS frontend

A154859 Decimal expansion of log_9 (17).

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.2894509615812829467581871223200888222408771473697233947468...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), this sequence, A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(17)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 17], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(17)/log(9) \\ G. C. Greubel, Sep 01 2018

A154947 Decimal expansion of log_9 (18).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.3154648767857287185497635571713804271497928200659402139353...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), this sequence, A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(18)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 18], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(18)/log(9) \\ G. C. Greubel, Sep 01 2018

Equals 1+A152747. - R. J. Mathar, Jan 07 2021

Equals A153495+1/2. - R. J. Mathar, Feb 15 2025

A155061 Decimal expansion of log_9 (19).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.3400719296231876724252833101095975652330714213471766109184...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), this sequence, A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(19)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 19], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(19)/log(9) \\ G. C. Greubel, Sep 01 2018

A155503 Decimal expansion of log_9 (20).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.3634165139304210206980473181820810524535518234649052723971...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), this sequence, A155676 (m=21), A155743 (m=22), A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(20)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 20], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(20)/log(9) \\ G. C. Greubel, Sep 01 2018

A155676 Decimal expansion of log_9 (21).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.3856218745807111300339641535412288590332356672971217396844...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), thus sequence, A155743 (m=22), A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(21)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9,21],10,120][[1]] (* Harvey P. Dale, May 04 2012 *)

default(realprecision, 100); log(21)/log(9) \\ G. C. Greubel, Sep 01 2018

A155743 Decimal expansion of log_9 (22).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.4067940461077977590742537645373448889212735826664123940539...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), this sequence, A155829 (m=23), A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(22)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 22], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(22)/log(9) \\ G. C. Greubel, Sep 01 2018

A155829 Decimal expansion of log_9 (23).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.4270249151001355537018158824746039413815908185252448835867...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), this sequence, A155976 (m=24).

SetDefaultRealField(RealField(100)); Log(23)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 23], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(23)/log(9) \\ G. C. Greubel, Sep 01 2018

A155976 Decimal expansion of log_9 (24).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.4463946303571861556492906715141412814493784601978206418059...

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for transcendental numbers

Cf. decimal expansion of log_9(m): A152747 (m=2), A153205 (m=5), A153495 (m=6), A153619 (m=7), A153756 (m=8), A154160 (m=10), A154181 (m=11), A154202 (m=12), A154339 (m=13), A154469 (m=14), A154578 (m=15), A154859 (m=17), A154947 (m=18), A155061 (m=19), A155503 (m=20), A155676 (m=21), A155743 (m=22), A155829 (m=23), this sequence.

SetDefaultRealField(RealField(100)); Log(24)/Log(9); // G. C. Greubel, Sep 01 2018

RealDigits[Log[9, 24], 10, 100][[1]] (* Vincenzo Librandi, Sep 01 2013 *)

default(realprecision, 100); log(24)/log(9) \\ G. C. Greubel, Sep 01 2018

A022331 Index of 2^n within sequence of numbers of form 2^i*3^j (A003586).

Original entry on oeis.org

1, 2, 4, 6, 9, 13, 17, 22, 28, 34, 41, 48, 56, 65, 74, 84, 95, 106, 118, 130, 143, 157, 171, 186, 202, 218, 235, 253, 271, 290, 309, 329, 350, 371, 393, 416, 439, 463, 487, 512, 538, 564, 591, 619, 647, 676, 706, 736, 767, 798, 830, 863, 896, 930, 965, 1000, 1036, 1072

Offset: 0

Clark Kimberling

nonn

Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Zak Seidov)
Norman Carey, Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet, arXiv preprint arXiv:1303.0888 [math.CO], 2013; Lambda Words: A Class of Rich Words Defined Over an Infinite Alphabet, J. Int. Seq. 16 (2013), Article 13.3.4.

Cf. A000079, A003586, A071521, A020915 (first differences), A152747.

Cf. A022330 (index of 3^n within A003586).

c[0] = 1; c[n_] := 1 + Sum[Ceiling[j*Log[3, 2]], {j, n}]; Table[c[i], {i, 0, 60}] (* Norman Carey, Jun 13 2012 *)

a(n)=my(t=1);1+n+sum(k=1,n,logint(t*=2,3)) \\ Ruud H.G. van Tol, Nov 25 2022

from sympy import integer_log
def A022331(n):
    m = 1<Chai Wah Wu, Sep 16 2024

a(n) = A071521(A000079(n)); A003586(a(n)) = A000079(n). - Reinhard Zumkeller, May 09 2006

a(n) ~ c * n^2, where c = log(2)/(2*log(3)) (A152747). - Amiram Eldar, Apr 07 2023

cp's OEIS Frontend

A154859 Decimal expansion of log_9 (17).

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A154947 Decimal expansion of log_9 (18).

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A155061 Decimal expansion of log_9 (19).

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A155503 Decimal expansion of log_9 (20).

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A155676 Decimal expansion of log_9 (21).

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A155743 Decimal expansion of log_9 (22).

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A155829 Decimal expansion of log_9 (23).

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A155976 Decimal expansion of log_9 (24).