This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005230 Stern's sequence: a(1) = 1, a(n+1) is the sum of the m preceding terms, where m*(m-1)/2 < n <= m*(m+1)/2 or equivalently m = ceiling((sqrt(8*n+1)-1)/2) = A002024(n). (Formerly M0785) 8
 1, 1, 2, 3, 6, 11, 20, 40, 77, 148, 285, 570, 1120, 2200, 4323, 8498, 16996, 33707, 66844, 132568, 262936, 521549, 1043098, 2077698, 4138400, 8243093, 16419342, 32706116, 65149296, 130298592, 260075635, 519108172, 1036138646, 2068138892, 4128034691 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A002487 is THE Stern's sequence! The subsequence of primes in this partial sum begins: 2, 3, 11, a(41) = 262364233421, and no more through a(200). - Jonathan Vos Post, Feb 18 2010 The next few primes are a(568), a(657), a(17765), ... with no further primes below a(50000). - Charles R Greathouse IV, Sep 19 2011 Lim_{n->inf} a(n)/2^n = 0.11756264240558743281779408719593950494049225979176... - Jon E. Schoenfield, Dec 17 2016 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 [extending prior submission by T. D. Noe] Jaegug Bae, Sungjin Choi, A generalization of a subset-sum-distinct sequence, J. Korean Math. Soc. 40 (2003), no. 5, 757-768. MR1996839 (2004d:05198). See d_1(n). G. Kreweras, Sur quelques problèmes relatifs au vote pondéré, [Some problems of weighted voting], Math. Sci. Humaines No. 84 (1983), 45-63. M. A. Stern, Aufgaben, J. Reine Angew. Math., 18 (1838), 100. FORMULA Partial sums give Conway-Guy sequence A005318. Cf. A066777. 2*a(n*(n+1)/2 + 1) = a(n*(n+1)/2 + 2) for n>=1; limit_{n->infty} a(n+1)/a(n) = 2. - Paul D. Hanna, Aug 28 2006 MAPLE A005230[1] := 1: n := 50: for k from 1 to n-1 do: A005230[k+1] := sum('A005230[j]', 'j'=k+1-(ceil((sqrt(8*k+1)-1)/2))..k): od: [seq(A005230[k], k=1..n)]; # UlrSchimke(AT)aol.com, Mar 16 2002 MATHEMATICA Module[{lst={1, 1}, n=2}, While[n<40, AppendTo[lst, Total[ Take[lst, -Ceiling[ (Sqrt[8n+1]-1)/2]]]]; n++]; lst] (* Harvey P. Dale, Apr 02 2012 *) PROG (PARI) a(n)=if(n==1, 1, sum(k=1, ceil((sqrt(8*n-7)-1)/2), a(n-k))) \\ Paul D. Hanna, Aug 28 2006 (PARI) v=vector(10^3); v[1]=v[2]=1; v[3]=2; v[4]=3; u=vector(#v, i, if(i>4, 0, sum(j=1, i, v[j]))); for(i=5, #v, m=ceil((sqrt(8*i-7)-1)/2); v[i]=u[i-1]-u[i-m-1]; u[i]=u[i-1]+v[i]); u=0; v \\ Charles R Greathouse IV, Sep 19 2011 CROSSREFS Cf. A002487. Sequence in context: A141435 A096080 A143658 * A030037 A077078 A077079 Adjacent sequences:  A005227 A005228 A005229 * A005231 A005232 A005233 KEYWORD core,easy,nonn,nice AUTHOR EXTENSIONS Name corrected by Mario Szegedy, Sep 15 1996 Name revised by Ulrich Schimke (ulrschimke(AT)aol.com), Mar 16 2002 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 October 21 08:16 EDT 2019. Contains 328292 sequences. (Running on oeis4.)