OFFSET
0,2
COMMENTS
Same digital roots as A065075 (sum of digits of the sum of the preceding numbers) and A004207 (sum of digits of all previous terms); they enter into the cycle {1 2 4 8 7 5}. - Alexandre Wajnberg, Dec 11 2005
It is believed that a(n) ~ n*9*log_10(2)/2, but this is an open problem. - N. J. A. Sloane, Apr 21 2013
The Radcliffe preprint shows that a(n) > log_4(n). - M. F. Hasler, May 18 2017
Sierpiński shows that if n >= A137284(k-1) then a(n) >= k (Problem 209). - David Radcliffe, Dec 26 2022
REFERENCES
Archimedeans Problems Drive, Eureka, 26 (1963), 12.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Zak Seidov, Table of n, a(n) for n = 0..10000
David Radcliffe, The growth of digital sums of powers of two. Preprint, 2015.
David G. Radcliffe, The growth of digital sums of powers of two, arXiv:1605.02839 [math.NT], 2016.
W. Sierpiński, 250 Problems in Elementary Number Theory, 1970.
C. L. Stewart, On the representation of an integer in two different bases, Journal für die reine und angewandte Mathematik 319 (1980): 63-72.
FORMULA
MAPLE
seq(convert(convert(2^n, base, 10), `+`), n=0..1000); # Robert Israel, Mar 29 2015
MATHEMATICA
Table[Total[IntegerDigits[2^n]], {n, 0, 55}] (* Vincenzo Librandi, Oct 08 2013 *)
PROG
(PARI) a(n)=sumdigits(2^n); \\ Michel Marcus, Nov 01 2013
(Python) [sum(map(int, str(2**n))) for n in range(56)] # David Radcliffe, Mar 29 2015
(Haskell)
a001370 = a007953 . a000079 -- Reinhard Zumkeller, Aug 14 2015
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
STATUS
approved