cp's OEIS Frontend

A228237 Numbers n for which there exists such a natural number k > n that k + bitcount(k) = n + bitcount(n), where bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

%I A228237 #9 Sep 13 2013 03:34:12
%S A228237 3,11,14,15,19,27,29,31,35,43,46,47,51,59,62,67,75,78,79,83,91,93,95,
%T A228237 99,107,110,111,115,123,124,125,126,127,131,139,142,143,147,155,157,
%U A228237 159,163,171,174,175,179,187,190,195,203,206,207,211,219,221,223,227
%N A228237 Numbers n for which there exists such a natural number k > n that k + bitcount(k) = n + bitcount(n), where bitcount(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.
%C A228237 In other words, all such terms A228236(n) which satisfy A228236(n) < A228087(A092391(A228236(n))).
%C A228237 Note: 124 is the first term that occurs both here and in A228091.
%H A228237 Antti Karttunen, <a href="/A228237/b228237.txt">Table of n, a(n) for n = 1..10000</a>
%e A228237 For cases 0 + A000120(0) = 0, 1 + A000120(1) = 2, 2 + A000120(2) = 3 there are no larger solutions yielding the same result.
%e A228237 However, for 3 + A000120(3) = 5 there is a larger solution yielding the same result, namely 4 + A000120(4) = 5, thus 3 is the first term of this sequence.
%e A228237 Next time this occurs for 11, as 11 + A000120(11) = 14 = 12 + A000120(12), and 12 > 11.
%o A228237 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A228237 (define A228237 (MATCHING-POS 1 1 (lambda (n) (< n (A228087 (A092391 n))))))
%Y A228237 Subset of A228236. Cf. also A228091.
%K A228237 nonn
%O A228237 1,1
%A A228237 _Antti Karttunen_, Sep 11 2013