%I #15 Oct 12 2013 22:01:30

%S 0,1,2,5,6,7,8,9,10,13,18,21,22,23,24,25,26,30,33,37,38,39,40,41,42,

%T 45,50,53,54,55,56,57,58,61,63,64,66,69,70,71,72,73,74,77,82,85,86,87,

%U 88,89,90,94,97,101,102,103,104,105,106,109,114,117,118,119,120

%N Numbers k for which a sum k + bitcount(k) cannot be obtained as a sum k2 + bitcount(k2) for any other k2<>k . Here bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

%C In other words, numbers k such that A228085(A092391(k)) = 1.

%H Antti Karttunen, <a href="/A228090/b228090.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%e 0 is in this sequence because the sum 0+A000120(0)=0 cannot be obtained with any other value of k than k=0.

%e 1 is in this sequence because the sum 1+A000120(1)=2 cannot be obtained with any other value of k than k=1.

%e 2 is in this sequence because the sum 2+A000120(2)=3 cannot be obtained with any other value of k than k=2.

%e 3 is not in this sequence because the sum 3+A000120(3)=5 can also be obtained with value k=4, as also 4+A000120(4)=5.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library) (define A228090 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 (A092391 k))))))

%Y Sequence A228089 sorted into ascending order. Complement: A228236.

%Y Cf. also A092391, A228085, A228088.

%K nonn,base

%O 1,3

%A _Antti Karttunen_, Aug 17 2013