A004655 - OEIS

%I #26 Jan 27 2023 10:15:21

%S 1,2,4,8,10,20,40,80,100,200,400,800,1000,2000,4000,8000,10000,20000,

%T 40000,80000,100000,200000,400000,800000,1000000,2000000,4000000,

%U 8000000,10000000,20000000,40000000,80000000

%N Powers of 2 written in base 16.

%C 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

%H G. C. Greubel, <a href="/A004655/b004655.txt">Table of n, a(n) for n = 0..2500</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,10).

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

%F From _Chai Wah Wu_, Sep 03 2020: (Start)

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

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

%t Table[FromDigits[IntegerDigits[2^n, 16]], {n, 50}] (* _G. C. Greubel_, Sep 11 2018 *)

%o (PARI) apply( a(n)=2^(n%4)*10^(n\4), [0..30]) \\ _M. F. Hasler_, Jun 22 2018

%o (Magma) [Seqint(Intseq(2^n, 16)): n in [0..30]]; // _G. C. Greubel_, Sep 10 2018

%o (Python)

%o def A004655(n): return 10**(n>>2)<<(n&3) # _Chai Wah Wu_, Jan 27 2023

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

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

%K nonn,base,easy

%O 0,2

%A _N. J. A. Sloane_