This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A246057 a(n) = (5*10^n - 2)/3. 9
 1, 16, 166, 1666, 16666, 166666, 1666666, 16666666, 166666666, 1666666666, 16666666666, 166666666666, 1666666666666, 16666666666666, 166666666666666, 1666666666666666, 16666666666666666, 166666666666666666, 1666666666666666666, 16666666666666666666 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(k-1) = (10^k - 4)/6, together with b(k) = 3*a(k-1) + 2 = A093143(k) and c(k) = 2*a(k-1) + 1 = A002277(k) are k-digit numbers for k >= 1 satisfying the so-called curious cubic identity a(k-1)^3 + b(k)^3 + c(k)^3 = a(k)*10^(2*k) + b(k)*10^k + c(k) (concatenated a(k)b(k)c(k)). This k-family and the proof of the identity has been given in the introduction of the van der Poorten reference. Thanks go to S. Heinemeyer for bringing these identities to my attention. - Wolfdieter Lang, Feb 07 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 A. van der Poorten, K. Thomsen, and M. Wiebe, A curious cubic identity and self-similar sums of squares, The Mathematical Intelligencer, v.29(2), pp. 39-41, March 2007. Index entries for linear recurrences with constant coefficients, signature (11,-10). FORMULA G.f.: (1 + 5*x)/((1 - x)*(1 - 10*x)). a(n) = 11*a(n-1) - 10*a(n-2). EXAMPLE Curious cubic identities (see a comment and reference above): 1^3 + 5^3 + 3^3 = 153, 16^3 + 50^3 + 33^3 = 165033, 166^3 + 500^3 + 333^3 = 166500333, ... - Wolfdieter Lang, Feb 07 2017 MATHEMATICA Table[(5 10^n - 2)/3, {n, 0, 20}] PROG (MAGMA) [(5*10^n-2)/3: n in [0..20]]; (PARI) vector(50, n, (5*10^(n-1)-2)/3) \\ Derek Orr, Aug 13 2014 CROSSREFS Cf. sequences with terms of the form 1k..k where the digit k is repeated n times: A000042 (k=1), A090843 (k=2), A097166 (k=3), A099914 (k=4), A099915 (k=5), this sequence (k=6), A246058 (k=7), A246059 (k=8), A067272 (k=9). Cf. A002277, A093143. Sequence in context: A204031 A025930 A125404 * A265598 A021744 A025445 Adjacent sequences:  A246054 A246055 A246056 * A246058 A246059 A246060 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Aug 13 2014 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 March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)