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Numbers k for which a sum k+bitcount(k) can be also obtained as a sum k2 +bitcount(k2) for some other k2<>k . Here bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.
4

%I #10 Sep 14 2013 12:42:58

%S 3,4,11,12,14,15,16,17,19,20,27,28,29,31,32,34,35,36,43,44,46,47,48,

%T 49,51,52,59,60,62,65,67,68,75,76,78,79,80,81,83,84,91,92,93,95,96,98,

%U 99,100,107,108,110,111,112,113,115,116,123,124,125,126,127,128

%N Numbers k for which a sum k+bitcount(k) can be also obtained as a sum k2 +bitcount(k2) for some 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="/A228236/b228236.txt">Table of n, a(n) for n = 1..10000</a>

%e 0 is not 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 not 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 not 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 in this sequence because the sum 3+A000120(3)=5 can also be obtained with value k=4, as also 4+A000120(4)=5, and thus also 4 is in this sequence.

%o (Scheme, with _Antti Karttunen_'s IntSeq-library) (define A228236 (MATCHING-POS 1 0 (lambda (k) (> (A228085 (A092391 k)) 1))))

%Y Complement: A228090. Subsets: A228091, A228237. Cf. also A092391, A228085.

%K nonn

%O 1,1

%A _Antti Karttunen_, Aug 17 2013