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

129, 134, 386, 391, 515, 518, 642, 647, 899, 904, 1028, 1030, 1154, 1159, 1411, 1416, 1540, 1543, 1667, 1672, 1924, 1929, 2178, 2183, 2435, 2440, 2564, 2567, 2691, 2696, 2948, 2953, 3077, 3079, 3203, 3208, 3460, 3465, 3589, 3592, 3716, 3721, 3973, 3978, 4226

Offset: 1

Author

N. J. A. Sloane, Oct 10 2013

Keywords

• nonn
• base

Comments

The positions of entries equal to 3 in A228085, or numbers that appear exactly thrice in A092391.

Numbers that can be expressed as the sum of distinct terms of the form 2^n+1, n=0,1,... in exactly three ways.

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller)
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A000120, A010061, A228088, A230058, A230091.

Cf. A227915.

Programs

Haskell

a230092 n = a230092_list !! (n-1)
a230092_list = filter ((== 3) . a228085) [1..]
-- Reinhard Zumkeller, Oct 13 2013

Maple

For Maple code see A230091.

Mathematica

nt = 1000; (* number of terms to produce *)
S[kmax_] := S[kmax] = Table[k + Total[IntegerDigits[k, 2]], {k, 0, kmax}] // Tally // Select[#, #[[2]] == 3&][[All, 1]]& // PadRight[#, nt]&;
S[nt];
S[kmax = 2 nt];
While[S[kmax] =!= S[kmax/2], kmax *= 2];
S[kmax] (* Jean-François Alcover, Mar 04 2023 *)