A067482 Powers of 4 with initial digit 4.

4, 4096, 4194304, 4294967296, 4398046511104, 4503599627370496, 4611686018427387904, 4722366482869645213696, 4835703278458516698824704, 4951760157141521099596496896, 401734511064747568885490523085290650630550748445698208825344

Offset: 1

Author

Amarnath Murthy, Feb 09 2002

Keywords

• base
• easy
• nonn

Comments

Appearances to the contrary, this sequence is not recursive with a geometric progression factor of 1024. Examples of a(n+1)/a(n) which are not 1024 are a(10)/a(9) = a(20)/a(19) = a(30)/a(29) = a(57)/a(56) = a(67)/a(66) = 2^106 or a(39)/a(38) = a(48)/a(47)= a(86)/a(85) = 2^116. - R. J. Mathar, Jan 10 2008

Therefore this sequence differs from A013830. - Georg Fischer, Oct 06 2018

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..71
• Tanya Khovanova, Non Recursions

Crossrefs

Cf. A000302, A067483, A013830, A242594.

Programs

GAP

Filtered(List([0..100],n->4^n),i->ListOfDigits(i)[1]=4); # Muniru A Asiru, Oct 06 2018

Mathematica

DeleteCases[Table[If[StringStartsQ[ToString[4^n],"4"],4^n], {n, 100}], Null] (* Stefano Spezia, Oct 06 2018 *)

Formula

a(n) = 4^A242594(n).