A098871 Sums of distinct powers of 4 plus 1.

1, 2, 5, 6, 17, 18, 21, 22, 65, 66, 69, 70, 81, 82, 85, 86, 257, 258, 261, 262, 273, 274, 277, 278, 321, 322, 325, 326, 337, 338, 341, 342, 1025, 1026, 1029, 1030, 1041, 1042, 1045, 1046, 1089, 1090, 1093, 1094, 1105, 1106, 1109, 1110, 1281, 1282, 1285, 1286

Offset: 0

Author

Tom C. Brown (tbrown(AT)sfu.ca), Oct 13 2004

Keywords

• nonn

Links

• Lukasz Merta, Composition inverses of the variations of the Baum-Sweet sequence, arXiv:1803.00292 [math.NT], 2018. See u(n) p. 11.

Crossrefs

Cf. A003278.

Programs

Maple

a:= proc(n) local m, r, b; m, r, b:= n, 1, 1;
      while m>0 do r:= r+b*irem(m, 2, 'm'); b:= b*4 od; r
    end:
seq(a(n), n=0..100); # Alois P. Heinz, Aug 17 2013

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"]; (* then *) Take[ Sort[ Plus @@@ Subsets[ Table[4^n, {n, 0, 5}]]] + 1, 50] (* Robert G. Wilson v, Oct 23 2004 *)
Total/@Subsets[4^Range[0,5],10]+1//Union (* Harvey P. Dale, May 03 2019 *)

Formula

a(n) = A000695(n) + 1. - Franklin T. Adams-Watters, Aug 17 2013

Extensions

More terms from Robert G. Wilson v, Oct 23 2004