OFFSET
0,1
COMMENTS
Every odd number m>=9 is a unique sum of the form a(k)+2a(l); moreover this sequence is the unique one with such property. In connection with A103151, note that there is no subsequence T of primes such that every odd number m>=9 is expressible as a unique sum of the form m=p+2q, where p and q are in T. One can prove that if one replaces 9 by any integer x_o>9, the statement remains true (see the Shevelev link).
LINKS
Vladimir Shevelev, On Unique Additive Representations of Positive Integers and Some Close Problems, arXiv:0811.0290 [math.NT], 2008.
MATHEMATICA
(* b = A000695 *) b[n_] := If[n==0, 0, If[EvenQ[n], 4 b[n/2] , b[n-1]+1]];
a[n_] := 2 b[n] + 3; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Dec 14 2018 *)
PROG
(PARI) a000695(n) = fromdigits(binary(n), 4);
a(n) = 2*a000695(n)+3; \\ Michel Marcus, Dec 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Nov 07 2008
EXTENSIONS
More terms from Michel Marcus, Dec 13 2018
STATUS
approved