A153596 -id:A153596 - cp's OEIS frontend

A154203 Decimal expansion of log_10 (12).

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

Offset: 1

N. J. A. Sloane, Oct 30 2009

			1.0791812460476248277225056927041013627365086271149129474507...

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

Cf. decimal expansion of log_10(m): A007524 (m=2), A114490 (m=3), A114493 (m=4), A153268 (m=5), A153496 (m=6), A153620 (m=7), A153790 (m=8), A104139 (m=9), A154182 (m=11), this sequence, A154368 (m=13), A154478 (m=14), A154580 (m=15), A154794 (m=16), A154860 (m=17), A154953 (m=18), A155062 (m=19), A155522 (m=20), A155677 (m=21), A155746 (m=22), A155830 (m=23), A155979 (m=24).

RealDigits[Log[10,12],10,100][[1]] (* Vincenzo Librandi,  Sep 11 2013 *)

log(12)/log(10) \\ Charles R Greathouse IV, Aug 04 2020

Equals A007524 + A153596. - R. J. Mathar, Jan 07 2021

A166465 a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 5.

Original entry on oeis.org

1, 5, 3, 15, 9, 45, 27, 135, 81, 405, 243, 1215, 729, 3645, 2187, 10935, 6561, 32805, 19683, 98415, 59049, 295245, 177147, 885735, 531441, 2657205, 1594323, 7971615, 4782969, 23914845, 14348907, 71744535, 43046721, 215233605, 129140163

Offset: 1

Klaus Brockhaus, Oct 14 2009

Interleaving of A000244 and A005030.
Second binomial transform is A054485.
Fifth binomial transform is A153596.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,3).

Cf. A000244 (powers of 3), A005030 (5*3^n), A054485, A153596, A162813.

[ n le 2 select 4*n-3 else 3*Self(n-2): n in [1..35] ];

LinearRecurrence[{0,3}, {1,5}, 41] (* G. C. Greubel, Jul 27 2024 *)

[3^(n/2)*(5*((n+1)%2) +sqrt(3)*(n%2))/3 for n in range(1,41)] # G. C. Greubel, Jul 27 2024

a(n) = (4 + (-1)^n) * 3^((2*n - 5 + (-1)^n)/4).
G.f.: x*(1+5*x)/(1-3*x^2).
a(n) = A162813(n-1), for n >= 2.
From G. C. Greubel, Jul 27 2024: (Start)
a(n) = (1/6)*3^(n/2)*( 5*(1+(-1)^n) + sqrt(3)*(1-(-1)^n) ).
E.g.f.: (1/3)*(sqrt(3)*sinh(sqrt(3)*x) + 10*(sinh(sqrt(3)*x/2))^2). (End)

cp's OEIS Frontend

A154203 Decimal expansion of log_10 (12).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula