cp's OEIS Frontend

A228090 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.

%I A228090 #15 Oct 12 2013 22:01:30
%S A228090 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 A228090 45,50,53,54,55,56,57,58,61,63,64,66,69,70,71,72,73,74,77,82,85,86,87,
%U A228090 88,89,90,94,97,101,102,103,104,105,106,109,114,117,118,119,120
%N A228090 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 A228090 In other words, numbers k such that A228085(A092391(k)) = 1.
%H A228090 Antti Karttunen, <a href="/A228090/b228090.txt">Table of n, a(n) for n = 1..10000</a>
%H A228090 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A228090 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 A228090 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 A228090 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 A228090 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 A228090 (Scheme, with _Antti Karttunen_'s IntSeq-library) (define A228090 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 (A092391 k))))))
%Y A228090 Sequence A228089 sorted into ascending order. Complement: A228236.
%Y A228090 Cf. also A092391, A228085, A228088.
%K A228090 nonn,base
%O A228090 1,3
%A A228090 _Antti Karttunen_, Aug 17 2013