A074116 -id:A074116 - cp's OEIS frontend

A074113 Duplicate of A074116.

8, 64, 512, 8192, 65536, 524288, 8388608, 67108864, 536870912, 8589934592, 68719476736, 549755813888, 8796093022208, 70368744177664, 562949953421312, 9007199254740992

Offset: 1

dead

A067488 Powers of 2 with initial digit 1.

Original entry on oeis.org

1, 16, 128, 1024, 16384, 131072, 1048576, 16777216, 134217728, 1073741824, 17179869184, 137438953472, 1099511627776, 17592186044416, 140737488355328, 1125899906842624, 18014398509481984, 144115188075855872, 1152921504606846976, 18446744073709551616

Offset: 1

Amarnath Murthy, Feb 09 2002

Also smallest n-digit power of 2.

For each range 10^(n-1) to 10^n-1 there exists exactly 1 power of 2 with first digit 1 (floor(log_10(a(n))) = n-1). As such, the density of this sequence relative to all powers of 2 (A000079) is log(2)/log(10) (0.301..., A007524), which is prototypical of Benford's Law. - Charles L. Hohn, Jul 23 2024

Muniru A Asiru, Table of n, a(n) for n = 1..993
Index to divisibility sequences

Cf. A000079, A067497, A055642,
Other initial digits: A067480, A067481, A067482, A067483, A067484, A067485, A067486, A067487, A074116.
Cf. A074117, A074118.

Filtered(List([0..60],n->2^n),i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018

[2^n: n in [0..100] | Intseq(2^n)[#Intseq(2^n)] eq 1]; // Vincenzo Librandi, Dec 31 2024

Select[2^Range[0, 70], First[IntegerDigits[#]] == 1 &]  (* Harvey P. Dale, Mar 14 2011 *)

a(n)=2^ceil((n-1)*log(10)/log(2)) \\ Charles R Greathouse IV, Apr 08 2012

(List.fill(50)(2: BigInt)).scanLeft(1: BigInt)( * ).filter(.toString.startsWith("1")) // _Alonso del Arte, Jan 16 2020

a(n) = 2^ceiling((n-1)*log(10)/log(2)). - Benoit Cloitre, Aug 29 2002
From Charles L. Hohn, Jun 09 2024: (Start)
a(n) = 2^A067497(n-1).
A055642(a(n)) = n. (End)

A074117 Smallest n-digit power of 3.

Original entry on oeis.org

1, 27, 243, 2187, 19683, 177147, 1594323, 14348907, 129140163, 1162261467, 10460353203, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089, 12157665459056928801

Offset: 1

Amarnath Murthy, Aug 27 2002

Andrew Howroyd, Table of n, a(n) for n = 1..200

Cf. A067488, A074116, A074118.

a(n) = 3^ceiling((n-1)*log(10)/log(3)). - Andrew Howroyd, Jan 16 2020

a(1) corrected and terms a(16) and beyond from Andrew Howroyd, Jan 16 2020

A074118 Largest power of 3 <= 10^n.

Original entry on oeis.org

1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 94143178827, 847288609443, 7625597484987, 68630377364883, 617673396283947, 5559060566555523, 50031545098999707, 450283905890997363

Offset: 0

Amarnath Murthy, Aug 27 2002

nonn

a(n)=3^d(n), with d(0)=0 and d(n)=A054965(n) if n>0. [Zak Seidov, Oct 01 2010]

Cf. A067488, A074116, A074117, A175852.

Table[3^Floor@Log[3, 10^n],{n,0,20}] (*Zak Seidov, Sep 29 2010*)

a(0)=1 and more terms from Zak Seidov, Sep 29 2010

cp's OEIS Frontend

A074113 Duplicate of A074116.

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A067488 Powers of 2 with initial digit 1.

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A074117 Smallest n-digit power of 3.

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A074118 Largest power of 3 <= 10^n.

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