A067497 Smallest power of 2 with n+1 digits (n>=0). Also numbers k such that 1 is the first digit of 2^k.

0, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 44, 47, 50, 54, 57, 60, 64, 67, 70, 74, 77, 80, 84, 87, 90, 94, 97, 100, 103, 107, 110, 113, 117, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 183, 187, 190, 193, 196

Offset

0,2

Comments

The asymptotic density of this sequence is log_10(2) = 0.301029... (A007524). - Amiram Eldar, Jan 27 2021

Links

Muniru A Asiru, Table of n, a(n) for n = 0..5000

Formula

a(n) = ceiling(n*log_2(10)). - Vladeta Jovovic, Jun 20 2002

Mathematica

a[n_] := Block[{k = 0}, While[ Floor[Log[10, 2^k] + 1] < n, k++ ]; k]; Table[ a[n], {n, 1, 61}]
Table[Ceiling[n*Log[2, 10]], {n, 0, 59}] (* Jean-François Alcover, Jan 29 2014, after Vladeta Jovovic *)

Prog

(PARI) for(n=0, 500, if(floor(2^n/10^(floor(n*log(2)/log(10))))==1, print1(n, ", ")))
(PARI) a(n) = ceil(n*log(10)/log(2)); \\ Michel Marcus, May 13 2017
(GAP) Filtered([0..200], n->ListOfDigits(2^n)[1]=1); # Muniru A Asiru, Oct 22 2018
(Python)
def A067497(n): return (10**n-1).bit_length() # Chai Wah Wu, Apr 02 2023

Crossrefs

Cf. A000079, A007524, A066343, A067480, A129344.

Sequence in context: A191402 A080600 A198266 * A123384 A138813 A310689

Adjacent sequences: A067494 A067495 A067496 * A067498 A067499 A067500

Keyword

base,nonn,easy

Author

Benoit Cloitre, Feb 22 2002

Extensions

Additional comments from Lekraj Beedassy, Jun 20 2002 and from Rick Shephard, Jun 27 2002

Status

approved