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A036555
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Number of bits of 3n in base 2.
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7
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0, 2, 2, 2, 2, 4, 2, 3, 2, 4, 4, 2, 2, 4, 3, 4, 2, 4, 4, 4, 4, 6, 2, 3, 2, 4, 4, 3, 3, 5, 4, 5, 2, 4, 4, 4, 4, 6, 4, 5, 4, 6, 6, 2, 2, 4, 3, 4, 2, 4, 4, 4, 4, 6, 3, 4, 3, 5, 5, 4, 4, 6, 5, 6, 2, 4, 4, 4, 4, 6, 4, 5, 4, 6, 6, 4, 4, 6, 5, 6, 4, 6, 6, 6, 6, 8, 2, 3, 2, 4, 4, 3, 3, 5, 4, 5, 2, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is also the largest integer such that 2^a(n) divides binomial(6n,3n)=A066802(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 27 2002
a(n) = A000120(A008585(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 03 2010]
a(A002450(n)) = 2*n.
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REFERENCES
| Flajolet, Philippe; Grabner, Peter; Kirschenhofer, Peter; Prodinger, Helmut; and Tichy, Robert F.; Mellin transforms and asymptotics: digital sums. Theoret. Comput. Sci. 123 (1994), 291-314.
D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969) 719-721.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)
Michael Gilleland, Some Self-Similar Integer Sequences
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MAPLE
| t1:=[];
for n from 0 to 100 do t2:=convert(3*n, base, 2); t3:=add(t2[i], i=1..nops(t2)); t1:=[op(t1), t3]; od:
t1;
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MATHEMATICA
| Total/@IntegerDigits[3Range[0, 100], 2] (* From Harvey P. Dale, Oct 03 2011 *)
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CROSSREFS
| Cf. A036556, A036557, A099033, A190944.
Sequence in context: A173439 A061389 A138011 * A046927 A084718 A154851
Adjacent sequences: A036552 A036553 A036554 * A036556 A036557 A036558
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KEYWORD
| nonn,base,nice
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AUTHOR
| Hoey(AT)AIC.NRL.Navy.Mil
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