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A261009 Write 2^n in base 3, add up the "digits". 5
1, 2, 2, 4, 4, 4, 4, 6, 4, 8, 8, 10, 10, 8, 10, 16, 12, 14, 12, 16, 14, 18, 16, 12, 10, 12, 14, 20, 20, 22, 24, 26, 24, 22, 22, 22, 18, 20, 26, 28, 28, 28, 26, 30, 30, 30, 26, 26, 26, 32, 38, 40, 38, 38, 28, 34, 40, 42, 38, 40, 46, 40, 38, 42, 48, 44, 42, 40, 42, 48, 48, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Comment from Jean-Paul Allouche, Oct 25 2015: As mentioned by Holdum et al. (2015) the following problem, cited in "Concrete Mathematics" by Graham, Knuth, and Patashnik (1994), is still open: prove that for all n > 256, binomial(2n,n) is either divisible by 4 or by 9 (cf. A000984).  This can be easily reduced to show that, for all k >= 9, 2*a(k) - a(k+1) >= 4.  This has been proved up to huge values of k (Holdum et al. mention k = 10^{13}).

For additional information about the divisibility of binomial(2n,n) by squares see the comments and references in A000984, - N. J. A. Sloane, Oct 29 2015

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..10000

Cernenoks J., Iraids J., Opmanis M., Opmanis R., Podnieks K., Integer complexity: experimental and analytical results II, arXiv:1409.0446 [math.NT] (September 2014)

Ronald L. Graham, Donald E. Knuth and Oren Patashnik, Concrete Math., 2n-d ed.; Addison-Wesley, 1994

Sebastian Tim Holdum, Frederik Ravn Klausen, Peter Michael Reichstein Rasmussen, Powers in prime bases and a problem on central coefficients, Integers 15 (2015), #A43

K. Podnieks, Digits of pi: limits to the seeming randomness, arXiv:1411.3911 [math.NT], 2014.

FORMULA

a(n) = A053735(A000079(n)). - Michel Marcus, Aug 14 2015

EXAMPLE

2^7 = 128_10 = 11202_3, so a(7) = 1+1+2+0+2 = 6.

MAPLE

S:=n->add(i, i in convert(2^n, base, 3)); [seq(S(n), n=0..100)];

MATHEMATICA

Table[Total@ IntegerDigits[2^n, 3], {n, 0, 100}] (* Giovanni Resta, Aug 14 2015 *)

PROG

(PARI) a(n) = vecsum(digits(2^n, 3)); \\ Michel Marcus, Aug 14 2015

(Haskell)

a261009 = a053735 . a000079  -- Reinhard Zumkeller, Aug 14 2015

CROSSREFS

Cf. A000079, A000984, A053735, A007089.

Sum of digits of k^n in base b for various pairs (k,b): A001370 (2,10), A011754 (3,2), A261009 (2,3), A261010 (5,3).

Sequence in context: A080374 A165040 A035683 * A239896 A001670 A100144

Adjacent sequences:  A261006 A261007 A261008 * A261010 A261011 A261012

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Aug 14 2015

STATUS

approved

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Last modified May 26 15:54 EDT 2018. Contains 304608 sequences. (Running on oeis4.)