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A233564 c-squarefree 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of terms in interval [2^(n-1), 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

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Last modified October 14 11:47 EDT 2019. Contains 327996 sequences. (Running on oeis4.)