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 A308900 An explicit example of an infinite sequence with a(1)=1 and, for n >= 2, a(n) and S(n) = Sum_{i=1..n} a(i) have no digit in common. 2
 1, 6, 4, 66, 34, 666, 334, 6666, 3334, 66666, 33334, 666666, 333334, 6666666, 3333334, 66666666, 33333334, 666666666, 333333334, 6666666666, 3333333334, 66666666666, 33333333334, 666666666666, 333333333334, 6666666666666, 3333333333334, 66666666666666, 33333333333334 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Used in a proof that the initial terms of A309151 are correct. The S(n) sequence is 1, 7, 11, 77, 111, 777, 1111, 7777, 11111, 77777, ... A093137 interleaved with positive terms of A002280. - Felix Fröhlich, Jul 15 2019 LINKS Robert Israel, Table of n, a(n) for n = 1..1999 R. Israel, Re: Help with a(n) and a cumulative sum, Seqfan (Jul 15 2019). Index entries for linear recurrences with constant coefficients, signature (-1,10,10). FORMULA For even n >= 2, a(n) = 6666...66 (with n/2 6's). For odd n >= 5, a(n) = 3333...334 (with (n-3)/2 3's and a single 4). From Robert Israel, Jul 15 2019: (Start) G.f. (1+7*x)/((1+x)*(1-10*x^2)). a(n) = -a(n - 1) + 10*a(n - 2) + 10*a(n - 3). (End) a(-n) = a(n+1). - Paul Curtz, Jul 18 2019 a(n) = (1/60)*(-40*(-1)^n + (1 + (-1)^n)*(2^(2+n/2)*5^(1+n/2)) + (1 + (-1)^(n+1))*10^((1+n)/2)). - Stefano Spezia, Jul 20 2019 MAPLE 1, seq(op([6*(10^i-1)/9, 3*(10^i-1)/9+1]), i=1..30); # Robert Israel, Jul 15 2019 MATHEMATICA CoefficientList[Series[(1 + 7 x)/((1 + x) (1 - 10 x^2)), {x, 0, 26}], x] (* Michael De Vlieger, Jul 18 2019 *) LinearRecurrence[{-1, 10, 10}, {1, 6, 4}, 30] (* Harvey P. Dale, Jan 02 2022 *) PROG (PARI) Vec((1+7*x)/((1+x)*(1-10*x^2)) + O(x^20)) \\ Felix Fröhlich, Jul 15 2019 (PARI) a(n) = if(n==1, 1, if(n%2==0, 6*(10^(n/2)-1)/9, 3*(10^((n-1)/2)-1)/9+1)) \\ Felix Fröhlich, Jul 15 2019 (Magma) I:=[1, 6, 4]; [n le 3 select I[n] else - Self(n-1) + 10*Self(n-2) + 10*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Ul 20 2019 CROSSREFS Cf. A002280, A093137, A309151. Cf. A289404. Sequence in context: A260716 A112521 A192350 * A354949 A239861 A266850 Adjacent sequences: A308897 A308898 A308899 * A308901 A308902 A308903 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane, Jul 15 2019 STATUS approved

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Last modified May 24 22:09 EDT 2024. Contains 372782 sequences. (Running on oeis4.)