This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A271528 a(n) = 2*(10^n - 1)^2/27. 1
 0, 6, 726, 73926, 7405926, 740725926, 74073925926, 7407405925926, 740740725925926, 74074073925925926, 7407407405925925926, 740740740725925925926, 74074074073925925925926, 7407407407405925925925926, 740740740740725925925925926, 74074074074073925925925925926 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS All terms are multiple of 6. Converges in a 10-adic sense to ...925925925926. A transformation of the Wonderful Demlo numbers (A002477). More generally, the ordinary generating function for the transformation of the Wonderful Demlo numbers, is k*x*(1 + 10*x)/(1 - 111*x + 1110*x^2 - 1000*x^3). LINKS Ilya Gutkovskiy, Transformation of the Wonderful Demlo numbers Eric Weisstein's World of Mathematics, Demlo Number Eric Weisstein's World of Mathematics, Repunit Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000). FORMULA O.g.f.: 6*x*(1 + 10*x)/(1 - 111*x + 1110*x^2 - 1000*x^3). E.g.f.: 2 (exp(x) - 2*exp(10*x) + exp(100*x))/27. a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3). a(n) = 6*A002477(n) = 6*A002275(n)^2 = A002276(n)*A002277(n) = sqrt(A075411(n)*A075412(n)). Sum_{n>=1} 1/a(n) = 0.1680577405662077350849154881928636039793563... Lim_{n -> infinity} a(n + 1)/a(n) = 100. EXAMPLE n=1:                  6 = 2 * 3; n=2:                726 = 22 * 33; n=3:              73926 = 222 * 333; n=4:            7405926 = 2222 * 3333; n=5:          740725926 = 22222 * 33333; n=6:        74073925926 = 222222 * 333333; n=7:      7407405925926 = 2222222 * 3333333; n=8:    740740725925926 = 22222222 * 33333333; n=9:  74074073925925926 = 222222222 * 333333333, etc. MATHEMATICA Table[2 ((10^n - 1)^2/27), {n, 0, 15}] LinearRecurrence[{111, -1110, 1000}, {0, 6, 726}, 16] PROG (PARI) x='x+O('x^99); concat(0, Vec(6*x*(1+10*x)/(1-111*x+1110*x^2-1000*x^3))) \\ Altug Alkan, Apr 09 2016 (Python) for n in xrange(0, 10**1):print((int)((2*(10**n-1)**2)/27)) # Soumil Mandal, Apr 10 2016 CROSSREFS Cf. A002275, A002276, A002277, A002477. Cf. similar sequences of the form k*((10^n - 1)/9)^2: A075411 (k=4), this sequence (k=6), A075412 (k=9), A075413 (k=16), A178630 (k=18), A075414 (k=25), A178631 (k=27), A075415 (k=36), A178632 (k=45), A075416 (k=49), A178633 (k=54), A178634 (k=63), A075417 (k=64), A178635 (k=72), A059988 (k=81). Sequence in context: A080369 A036981 A202080 * A316748 A232130 A289365 Adjacent sequences:  A271525 A271526 A271527 * A271529 A271530 A271531 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Apr 09 2016 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 01:47 EDT 2018. Contains 316405 sequences. (Running on oeis4.)