A183226 - OEIS

%I #18 Oct 29 2015 15:23:46

%S 1,2,4,4,4,4,8,4,4,8,12,12,12,12,8,12,16,20,20,20,16,12,20,24,28,20,

%T 32,32,24,32,40,40,32,24,28,32,32,40,28,36,36,40,44,40,36,40,36,44,44,

%U 44,44,48,52,52,48,56,40,56,68,60,52,52,48,60,56,64,60,48,56,60,60,64,60,60,60,64,52,48,64,68,56,80,80

%N Sum of digits of (2^n) in base 5, also sum of digits of (10^n) in base 5.

%C If i >= 2, a(n) mod 4 = 0. (Cf. A053824)

%H Robert Israel, <a href="/A183226/b183226.txt">Table of n, a(n) for n = 0..10000</a>

%e a(9) = 8 because 10^9 = 4022000000000_5, and 2^9 = 512 = 4022_5.

%p a:= n-> add(i, i=convert (2^n, base, 5)):

%p seq(a(n), n=0..82);  # _Alois P. Heinz_, Jan 06 2011

%t Table[Plus@@IntegerDigits[2^n, 5], {n, 0, 49}] (* Either that one or this one *) Table[Plus@@IntegerDigits[10^n, 5], {n, 0, 49}] (* _Alonso del Arte_, Jan 06 2011 *)

%o (PARI)\\  L is the list of the N digits of 2^n in quinary.

%o      \\ L[1] = a_0 , ..., L[N] = a_(N-1).

%o convert(n)={n=2^n; x=n; N=floor(log(n)/log(5))+1;

%o L = listcreate(N);

%o while(x, n=floor(n/5); r=x-5*n; listput(L, r); x=n; );

%o L; N};

%o for(n=0,100,convert(n);an=0;for(i=1,N,an+=L[i];); print1(an,", "));

%o (PARI) t(n) = if(n<1, 0, if(n%5, t(n-1)+1, t(n/5)));

%o vector(200, n, n--; t(2^n)) \\ _Altug Alkan_, Oct 28 2015

%Y Cf. A055476, A173670, A183227, A183228.

%K nonn,easy,base

%O 0,2

%A _Washington Bomfim_, Jan 01 2011