

A053754


If k is in the sequence then 2*k and 2*k+1 are not (and 0 is in the sequence); when written in binary k has an even number of bits (0 has 0 digits).


47



0, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148
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OFFSET

1,2


COMMENTS

Runs of successive terms with same number of bits have length twice powers of 4 (A081294). [Clarified by Michel Marcus, Oct 21 2020]
The lower and upper asymptotic densities of this sequence are 1/3 and 2/3, respectively.  Amiram Eldar, Feb 01 2021
Also numbers k such that the kth composition in standard order (row k of A066099) has even sum. The terms and corresponding compositions begin:
0: () 2: (2) 8: (4)
3: (1,1) 9: (3,1)
10: (2,2)
11: (2,1,1)
12: (1,3)
13: (1,2,1)
14: (1,1,2)
15: (1,1,1,1)
(End)


LINKS



MATHEMATICA

Select[Range[0, 150], EvenQ @ IntegerLength[#, 2] &] (* Amiram Eldar, Feb 01 2021 *)


PROG

(Haskell)
a053754 n = a053754_list !! (n1)
a053754_list = 0 : filter (even . a070939) [1..]
(PARI) lista(nn) = {my(va = vector(nn)); for (n=2, nn, my(k=va[n1]+1); while (#select(x>(x==k\2), va), k++); va[n] = k; ); va; } \\ Michel Marcus, Oct 20 2020
(PARI) a(n) = n1 + (1<<bitand(logint(6*n3, 2), 2))\3; \\ Kevin Ryde, Apr 30 2021


CROSSREFS

Positions of even terms in A029837 with offset 0.
The version for Heinz numbers of partitions is A300061, counted by A058696.


KEYWORD

base,easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



