A183226 Sum of digits of (2^n) in base 5, also sum of digits of (10^n) in base 5.

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, 32, 32, 24, 32, 40, 40, 32, 24, 28, 32, 32, 40, 28, 36, 36, 40, 44, 40, 36, 40, 36, 44, 44, 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

Offset

0,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

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

Maple

a:= n-> add(i, i=convert (2^n, base, 5)):
seq(a(n), n=0..82);  # Alois P. Heinz, Jan 06 2011

Mathematica

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 *)

Prog

(PARI)\\  L is the list of the N digits of 2^n in quinary.
     \\ L[1] = a_0 , ..., L[N] = a_(N-1).
convert(n)={n=2^n; x=n; N=floor(log(n)/log(5))+1;
L = listcreate(N);
while(x, n=floor(n/5); r=x-5*n; listput(L, r); x=n; );
L; N};
for(n=0, 100, convert(n); an=0; for(i=1, N, an+=L[i]; ); print1(an, ", "));
(PARI) t(n) = if(n<1, 0, if(n%5, t(n-1)+1, t(n/5)));
vector(200, n, n--; t(2^n)) \\ Altug Alkan, Oct 28 2015

Crossrefs

Cf. A055476, A173670, A183227, A183228.

Sequence in context: A194443 A220523 A220527 * A235863 A220495 A194441

Adjacent sequences: A183223 A183224 A183225 * A183227 A183228 A183229

Keyword

nonn,easy,base

Author

Washington Bomfim, Jan 01 2011

Status

approved