

A010061


Binary self or Colombian numbers: numbers that cannot be expressed as the sum of distinct terms of the form 2^k+1 (k>=0), or equivalently, numbers not of form m + sum of binary digits of m.


26



1, 4, 6, 13, 15, 18, 21, 23, 30, 32, 37, 39, 46, 48, 51, 54, 56, 63, 71, 78, 80, 83, 86, 88, 95, 97, 102, 104, 111, 113, 116, 119, 121, 128, 130, 133, 135, 142, 144, 147, 150, 152, 159, 161, 166, 168, 175, 177, 180, 183, 185, 192, 200, 207, 209, 212, 215, 217
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OFFSET

1,2


COMMENTS

No two consecutive values appear in this sequence (see Links).  Griffin N. Macris, May 31 2020


REFERENCES

Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, in preparation, 2017.
Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.24.


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000
Griffin N. Macris, Proof that no consecutive self numbers exist
Index entries for Colombian or self numbers and related sequences


MAPLE

# For Maple code see A230091.  N. J. A. Sloane, Oct 10 2013


MATHEMATICA

Table[n + Total[IntegerDigits[n, 2]], {n, 0, 300}] // Complement[Range[Last[#]], #]& (* JeanFrançois Alcover, Sep 03 2013 *)


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A010061 (ZEROPOS 1 0 A228085))
(Haskell)
a010061 n = a010061_list !! (n1)
a010061_list = filter ((== 0) . a228085) [1..]
 Reinhard Zumkeller, Oct 13 2013


CROSSREFS

Complement of A228082, or equally, numbers which do not occur in A092391. Gives the positions of zeros (those occurring after a(0)) in A228085A228087 and positions of ones in A227643. Leftmost column of A228083. Base10 analog: A003052.
Cf. A010062, A055938, A230091, A230092, A230058.
Cf. A228088, A227915, A232228.
Sequence in context: A247787 A074165 A137821 * A280557 A266665 A249715
Adjacent sequences: A010058 A010059 A010060 * A010062 A010063 A010064


KEYWORD

nonn,base


AUTHOR

Leonid Broukhis


EXTENSIONS

More terms from Antti Karttunen, Aug 17 2013
Better definition from Matthew C. Russell, Oct 08 2013


STATUS

approved



