

A233564


csquarefree numbers: positive integers which in binary are concatenation of distinct parts of the form 10...0 with nonnegative number of zeros.


5



1, 2, 4, 5, 6, 8, 9, 12, 16, 17, 18, 20, 24, 32, 33, 34, 37, 38, 40, 41, 44, 48, 50, 52, 64, 65, 66, 68, 69, 70, 72, 80, 81, 88, 96, 98, 104, 128, 129, 130, 132, 133, 134, 137, 140, 144, 145, 152, 160, 161, 176, 192, 194, 196, 200, 208, 256, 257, 258, 260, 261
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OFFSET

1,2


COMMENTS

Number of terms in interval [2^(n1), 2^n) is the number of compositions of n with distinct parts (cf. A032020). For example, if n=6, then interval [2^5, 2^6) contains 11 terms {32,...,52}. This corresponds to 11 compositions with distinct parts of 6: 6, 5+1, 1+5, 4+2, 2+4, 3+2+1, 3+1+2, 2+3+1, 2+1+3, 1+3+2, 1+2+3.


LINKS

Table of n, a(n) for n=1..61.
Index entries for sequences related to binary expansion of n


EXAMPLE

49 in binary has the following parts of the form 10...0 with nonnegative number of zeros: (1),(1000),(1). Two of them are the same. So it is not in the sequence. On the other hand, 50 has distinct parts (1)(100)(10), thus it is a term.


MATHEMATICA

bitPatt[n_]:=bitPatt[n]=Split[IntegerDigits[n, 2], #1>#2#2==0&];
Select[Range[300], bitPatt[#]==DeleteDuplicates[bitPatt[#]]&] (* Peter J. C. Moses, Dec 13 2013 *)


CROSSREFS

Cf. A032020, A124771, A233249, A233312, A233416, A233420, A233564, A233569, A233655.
Sequence in context: A188080 A048262 A285035 * A030326 A080086 A229133
Adjacent sequences: A233561 A233562 A233563 * A233565 A233566 A233567


KEYWORD

nonn,base


AUTHOR

Vladimir Shevelev, Dec 13 2013


EXTENSIONS

More terms from Peter J. C. Moses, Dec 13 2013


STATUS

approved



