The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A147568 a(n) = 2*A000695(n)+3. 2
 3, 5, 11, 13, 35, 37, 43, 45, 131, 133, 139, 141, 163, 165, 171, 173, 515, 517, 523, 525, 547, 549, 555, 557, 643, 645, 651, 653, 675, 677, 683, 685, 2051, 2053, 2059, 2061, 2083, 2085, 2091, 2093, 2179, 2181, 2187, 2189, 2211, 2213, 2219, 2221, 2563, 2565, 2571 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000695, A062880, A103151. Sequence in context: A260224 A105071 A089251 * A006794 A032457 A122564 Adjacent sequences:  A147565 A147566 A147567 * A147569 A147570 A147571 KEYWORD nonn AUTHOR Vladimir Shevelev, Nov 07 2008 EXTENSIONS More terms from Michel Marcus, Dec 13 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 14 04:20 EDT 2021. Contains 342941 sequences. (Running on oeis4.)