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

1,1

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

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 *)

Prog

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

Crossrefs

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

Cf. A227915.

Sequence in context: A298720 A025332 A025324 * A060878 A127337 A185347

Adjacent sequences: A230089 A230090 A230091 * A230093 A230094 A230095

Keyword

nonn,base

Author

N. J. A. Sloane, Oct 10 2013

Status

approved