cp's OEIS Frontend

A228088 Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.

%I A228088 #33 Jan 20 2020 21:42:24
%S A228088 0,2,3,7,8,9,10,11,12,16,20,24,25,26,27,28,29,34,35,40,41,42,43,44,45,
%T A228088 49,53,57,58,59,60,61,62,65,66,68,69,72,73,74,75,76,77,81,85,89,90,91,
%U A228088 92,93,94,99,100,105,106,107,108,109,110,114,118,122,123,124
%N A228088 Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1's in binary representation of nonnegative integer k.
%C A228088 wt(k) = A000120(k) is also called bitcount(k).
%C A228088 In other words, the positions of ones in A228085.
%C A228088 Numbers that can be expressed as the sum of distinct terms of the form 2^n+1, n=0,1,... in exactly one way. - _Matthew C. Russell_, Oct 08 2013
%H A228088 Antti Karttunen, <a href="/A228088/b228088.txt">Table of n, a(n) for n = 1..10000</a>
%H A228088 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A228088 a(n) = A092391(A228089(n)). [Consequence of the definitions of A228088 & A228089. Use the given Scheme-code to actually compute the sequence]
%e A228088 0 is in this sequence because there is a unique k such that k+A000120(k)=0, in this case k=0.
%e A228088 1 is not in this sequence because there is no such k that k+A000120(k) would be 1. (Instead 1 is in A010061).
%e A228088 2 is in this sequence because there is exactly one k that satisfies k+A000120(k)=2, namely k=1.
%e A228088 3 is in this sequence because there is exactly one k that satisfies k+A000120(k)=3, namely k=2.
%e A228088 4 is not in this sequence because there is no such k that k+A000120(k) would be 4. (Instead 4 is in A010061.)
%e A228088 5 is not in this sequence because there is more than one k that satisfies k+A000120(k)=5, namely k=3 and k=4.
%p A228088 For Maple code see A230091. - _N. J. A. Sloane_, Oct 10 2013
%o A228088 (Scheme with _Antti Karttunen_'s IntSeq-library)
%o A228088 (define A228088 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 k)))))
%o A228088 (Haskell)
%o A228088 a228088 n = a228088_list !! (n-1)
%o A228088 a228088_list = 0 : filter ((== 1) . a228085) [1..]
%o A228088 -- _Reinhard Zumkeller_, Oct 13 2013
%Y A228088 Subset of A228082.
%Y A228088 Cf. A228089 (corresponding k's for each a(n)).
%Y A228088 Cf. A228090 (the same k's sorted into ascending order).
%Y A228088 Cf. A000120, A228085, A092391, A010061, A010062, A230091, A230092, A230058.
%Y A228088 Cf. A227915.
%K A228088 nonn,base
%O A228088 1,2
%A A228088 _Antti Karttunen_, Aug 09 2013