A147818 - OEIS

%I #24 Mar 15 2024 02:20:13

%S 5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,

%T 9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,

%U 5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5,9,9,5,5

%N Period 4: repeat [5, 9, 9, 5].

%C Last digit of the number whose binary representation is the concatenation of n 1's, 2n-1 0's and n 1's.

%C a(n) is the final digit of A147539(n).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1).

%F a(n+1) = 7-2*cos(Pi*n/2)+2*sin(Pi*n/2). - _R. J. Mathar_, Oct 08 2011

%F a(n) = a(n-1)-a(n-2)+a(n-3) for n>3. G.f.: x*(5*x^2+4*x+5)/((1-x)*(x^2+1)). [_Colin Barker_, Nov 04 2012]

%F a(n) = a(n-4) for n>4. - _Wesley Ivan Hurt_, Jul 09 2016

%p A010879 := proc(n) n mod 10; end:

%p A147539 := proc(n) 2^n-1+2^(4*n-1)-2^(3*n-1); end:

%p A147818 := proc(n) A010879(A147539(n)); end: # _R. J. Mathar_, Jan 22 2009

%p seq(op([5, 9, 9, 5]), n=1..40); # _Wesley Ivan Hurt_, Jul 09 2016

%t PadRight[{}, 100, {5, 9, 9, 5}] (* _Wesley Ivan Hurt_, Jul 09 2016 *)

%o (Magma) &cat [[5, 9, 9, 5]^^30]; // _Wesley Ivan Hurt_, Jul 09 2016

%Y Cf. A138120, A147539.

%K base,easy,nonn

%O 1,1

%A _Omar E. Pol_, Nov 14 2008, Jan 25 2009

%E More terms from _R. J. Mathar_, Jan 22 2009