A004647 Powers of 2 written in base 8.

1, 2, 4, 10, 20, 40, 100, 200, 400, 1000, 2000, 4000, 10000, 20000, 40000, 100000, 200000, 400000, 1000000, 2000000, 4000000, 10000000, 20000000, 40000000, 100000000, 200000000, 400000000, 1000000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

Or, numbers of form 10^n, 2*10^n, 4*10^n.

Or, numbers n such that the digits of n^3 are decreasing. - Dmitry Kamenetsky, Jun 15 2006

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Thomas Harriot, Manuscript 6782, p. 1, c. 1599.
• D. Panario, M. Sahin, and Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.
• Index entries for linear recurrences with constant coefficients, signature (0,0,10).

Programs

Magma

[Seqint(Intseq(2^n, 8)): n in [0..30]]; // G. C. Greubel, Sep 10 2018

Mathematica

Table[FromDigits[IntegerDigits[2^n,8]],{n,0,30}] (* or *) LinearRecurrence[ {0,0,10},{1,2,4},30] (* Harvey P. Dale, Aug 16 2012 *)

PARI

a(n)=2^(n%3)*10^(n\3) \\ Charles R Greathouse IV, Oct 22 2014

Python

def A004647(n): return int(oct(2**n)[2:]) # Chai Wah Wu, May 23 2022

Formula

a(0)=1, a(1)=2, a(2)=4, a(n)=10*a(n-3). - Harvey P. Dale, Aug 16 2012

G.f.: (1 + 2*x + 4*x^2)/(1 - 10*x^3 ). - R. J. Mathar, Mar 13 2015