A228088 - OEIS

%I #33 Jan 20 2020 21:42:24

%S 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 49,53,57,58,59,60,61,62,65,66,68,69,72,73,74,75,76,77,81,85,89,90,91,

%U 92,93,94,99,100,105,106,107,108,109,110,114,118,122,123,124

%N 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 wt(k) = A000120(k) is also called bitcount(k).

%C In other words, the positions of ones in A228085.

%C 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 Antti Karttunen, <a href="/A228088/b228088.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>

%F a(n) = A092391(A228089(n)). [Consequence of the definitions of A228088 & A228089. Use the given Scheme-code to actually compute the sequence]

%e 0 is in this sequence because there is a unique k such that k+A000120(k)=0, in this case k=0.

%e 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 2 is in this sequence because there is exactly one k that satisfies k+A000120(k)=2, namely k=1.

%e 3 is in this sequence because there is exactly one k that satisfies k+A000120(k)=3, namely k=2.

%e 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 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 For Maple code see A230091. - _N. J. A. Sloane_, Oct 10 2013

%o (Scheme with _Antti Karttunen_'s IntSeq-library)

%o (define A228088 (MATCHING-POS 1 0 (lambda (k) (= 1 (A228085 k)))))

%o (Haskell)

%o a228088 n = a228088_list !! (n-1)

%o a228088_list = 0 : filter ((== 1) . a228085) [1..]

%o -- _Reinhard Zumkeller_, Oct 13 2013

%Y Subset of A228082.

%Y Cf. A228089 (corresponding k's for each a(n)).

%Y Cf. A228090 (the same k's sorted into ascending order).

%Y Cf. A000120, A228085, A092391, A010061, A010062, A230091, A230092, A230058.

%Y Cf. A227915.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, Aug 09 2013