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 A001370 Sum of digits of 2^n. (Formerly M1085 N0414) 41
 1, 2, 4, 8, 7, 5, 10, 11, 13, 8, 7, 14, 19, 20, 22, 26, 25, 14, 19, 29, 31, 26, 25, 41, 37, 29, 40, 35, 43, 41, 37, 47, 58, 62, 61, 59, 64, 56, 67, 71, 61, 50, 46, 56, 58, 62, 70, 68, 73, 65, 76, 80, 79, 77, 82, 92, 85, 80, 70, 77 (list; graph; refs; listen; history; text; internal format)
 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 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. 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 a(n) = A007953(A000079(n)). - Michel Marcus, Nov 01 2013 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 Cf. sum of digits of k^n: A004166 (k=3), A065713 (k=4), A066001(k=5), A066002 (k=6), A066003(k=7), A066004 (k=8), A065999 (k=9), A066005 (k=11), A066006 (k=12). Cf. A007953, A000079, A261009, A011754. Sequence in context: A225746 A021406 A065075 * A195715 A343629 A039794 Adjacent sequences: A001367 A001368 A001369 * A001371 A001372 A001373 KEYWORD base,easy,nonn AUTHOR STATUS approved

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Last modified December 7 05:31 EST 2022. Contains 358649 sequences. (Running on oeis4.)