A067488 Powers of 2 with initial digit 1.

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

Offset

1,2

Comments

Also smallest n-digit power of 2.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..993

Index to divisibility sequences

Formula

a(n) = 2^ceiling((n-1)*log(10)/log(2)). - Benoit Cloitre, Aug 29 2002

Mathematica

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

Prog

(PARI) a(n)=2^ceil((n-1)*log(10)/log(2)) \\ Charles R Greathouse IV, Apr 08 2012
(GAP) Filtered(List([0..60], n->2^n), i->ListOfDigits(i)[1]=1); # Muniru A Asiru, Oct 22 2018
(Scala) (List.fill(50)(2: BigInt)).scanLeft(1: BigInt)(_ * _).filter(_.toString.startsWith("1")) // Alonso del Arte, Jan 16 2020

Crossrefs

Cf. A000079, A067480, A067481, A067482, A067483, A067484, A067485, A067486, A074116, A074117, A074118.

Sequence in context: A128692 A132136 A163399 * A308310 A120785 A031156

Adjacent sequences: A067485 A067486 A067487 * A067489 A067490 A067491

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 09 2002

Status

approved