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A230092 Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k.

%I A230092 #20 Mar 04 2023 15:09:52
%S A230092 129,134,386,391,515,518,642,647,899,904,1028,1030,1154,1159,1411,
%T A230092 1416,1540,1543,1667,1672,1924,1929,2178,2183,2435,2440,2564,2567,
%U A230092 2691,2696,2948,2953,3077,3079,3203,3208,3460,3465,3589,3592,3716,3721,3973,3978,4226
%N A230092 Numbers of the form k + wt(k) for exactly three distinct k, where wt(k) = A000120(k) is the binary weight of k.
%C A230092 The positions of entries equal to 3 in A228085, or numbers that appear exactly thrice in A092391.
%C A230092 Numbers that can be expressed as the sum of distinct terms of the form 2^n+1, n=0,1,... in exactly three ways.
%H A230092 Reinhard Zumkeller and Donovan Johnson, <a href="/A230092/b230092.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Reinhard Zumkeller)
%H A230092 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%p A230092 For Maple code see A230091.
%t A230092 nt = 1000; (* number of terms to produce *)
%t A230092 S[kmax_] := S[kmax] = Table[k + Total[IntegerDigits[k, 2]], {k, 0, kmax}] // Tally // Select[#, #[[2]] == 3&][[All, 1]]& // PadRight[#, nt]&;
%t A230092 S[nt];
%t A230092 S[kmax = 2 nt];
%t A230092 While[S[kmax] =!= S[kmax/2], kmax *= 2];
%t A230092 S[kmax] (* _Jean-François Alcover_, Mar 04 2023 *)
%o A230092 (Haskell)
%o A230092 a230092 n = a230092_list !! (n-1)
%o A230092 a230092_list = filter ((== 3) . a228085) [1..]
%o A230092 -- _Reinhard Zumkeller_, Oct 13 2013
%Y A230092 Cf. A000120, A010061, A228088, A230058, A230091.
%Y A230092 Cf. A227915.
%K A230092 nonn,base
%O A230092 1,1
%A A230092 _N. J. A. Sloane_, Oct 10 2013