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!)
 A226089 Denominators of the series a(n+1) = (a(n)+k)/(1+a(n)*k); where k=1/(n+1), a(1)=1/2. 2
 2, 7, 11, 8, 11, 29, 37, 23, 28, 67, 79, 46, 53, 121, 137, 77, 86, 191, 211, 116, 127, 277, 301, 163, 176, 379, 407, 218, 233, 497, 529, 281, 298, 631, 667, 352, 371, 781, 821, 431, 452, 947, 991, 518, 541, 1129, 1177, 613, 638, 1327, 1379, 716, 743, 1541 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence shares numerators with the Harary numbers, A160050. This is the sequence 1/2 + 1/3 + 1/4 +...+1/n using relativistic velocity addition, where the addition of velocities a and b = (a+b) / (1 + a*b/c^2). That is, for objects traveling at c/2 + c/3 + ... +c/n relative to each other, the n-th object has velocity A160050(n)/a(n)*c relative to a stationary observer. LINKS Christian N. K. Anderson, Table of n, a(n) for n = 1..10000 Christian N. K. Anderson, Ulam Spiral of the first 4000 terms. Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1). FORMULA G.f.: -x*(x^8-2*x^7+4*x^6-6*x^5+7*x^4-3*x^3+2*x^2+x+2) / ((x-1)^3*(x^2+1)^3). - Colin Barker, Jul 18 2015 EXAMPLE a(10) = a(9) + 1/11 using relativistic velocity addition. Since a(9) = 27/28, the sum is (27/28 + 1/11) / (1 + 27/28 * (1/11)) = (325 / 308) / (335/308) = 65/67. PROG (R) library(gmp); reladd<-function(x, y) (x+y)/(1+x*y)y=as.bigq(rep(1, 100)); y[1]=y[1]/2; for(i in 2:100) y[i]=reladd(y[i-1], y[i]/(i+1)); denominator(y) (PARI) Vec(-x*(x^8-2*x^7+4*x^6-6*x^5+7*x^4-3*x^3+2*x^2+x+2) / ((x-1)^3*(x^2+1)^3) + O(x^100)) \\ Colin Barker, Jul 18 2015 CROSSREFS Cf. A160050, A001844. Sequence in context: A020638 A091385 A053247 * A208846 A087723 A299242 Adjacent sequences:  A226086 A226087 A226088 * A226090 A226091 A226092 KEYWORD nonn,easy AUTHOR Rick G. Rosner, Christian N. K. Anderson, and Kevin L. Schwartz, May 25 2013 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 June 14 14:21 EDT 2021. Contains 345025 sequences. (Running on oeis4.)