A004655 Powers of 2 written in base 16.

1, 2, 4, 8, 10, 20, 40, 80, 100, 200, 400, 800, 1000, 2000, 4000, 8000, 10000, 20000, 40000, 80000, 100000, 200000, 400000, 800000, 1000000, 2000000, 4000000, 8000000, 10000000, 20000000, 40000000, 80000000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

10^(Floor[n/4]) | a(n). The first term of each value cycles the pattern {1, 2, 4, 8}. - G. C. Greubel, Sep 10 2018

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,10).

Crossrefs

Cf. A000079, A004643, ..., A004654: powers of 2 written in base 10, 4, 5, ..., 15.

Cf. A000244, A004656, A004658, A004659, ... : powers of 3 in base 10, 2, 4, 5, ...

Programs

Magma

[Seqint(Intseq(2^n, 16)): n in [0..30]]; // G. C. Greubel, Sep 10 2018

Mathematica

Table[FromDigits[IntegerDigits[2^n, 16]], {n, 50}] (* G. C. Greubel, Sep 11 2018 *)

PARI

apply( a(n)=2^(n%4)*10^(n\4), [0..30]) \\ M. F. Hasler, Jun 22 2018

Python

def A004655(n): return 10**(n>>2)<<(n&3) # Chai Wah Wu, Jan 27 2023

Formula

a(n) = 2^(n mod 4)*10^floor(n/4). - M. F. Hasler, Jun 22 2018

From Chai Wah Wu, Sep 03 2020: (Start)

a(n) = 10*a(n-4) for n > 3.

G.f.: -(2*x + 1)*(4*x^2 + 1)/(10*x^4 - 1). (End)