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 A110365 a(1)=2, a(n+1) = a(n)*A010888(a(n)). 1
 2, 4, 16, 112, 448, 3136, 12544, 87808, 351232, 2458624, 9834496, 68841472, 275365888, 1927561216, 7710244864, 53971714048, 215886856192, 1511207993344, 6044831973376, 42313823813632, 169255295254528, 1184787066781696, 4739148267126784, 33174037869887488 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From a(2) onwards, the digital root follows the pattern alternately 4,7,4,7,4,7,... LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,28). FORMULA a(1) = 2, a(2) = 4, a(3) = 16. a(2*n) = 4*a(2*n-1), a(2*n+1) = 7*a(2*n) for n > 1. From Colin Barker, May 05 2016: (Start) a(n) = 2^(-1+n)*(7^(1/2*(-3+n))*(2-2*(-1)^n + sqrt(7) + (-1)^n*sqrt(7))) for n > 1. a(n) = 2^n*7^(n/2-1) for n > 1 and even. a(n) = 2^(n+1)*7^((n-3)/2) for n > 1 and odd. a(n) = 28*a(n-2) for n > 3. G.f.: 2*x*(1+2*x-20*x^2) / (1-28*x^2). (End) E.g.f.: (-7 + 70*x + 7*cosh(2*Sqrt(7)*x) + 2*sqrt(7)*sinh(2*sqrt(7)*x))/49. - Ilya Gutkovskiy, May 05 2016 MATHEMATICA k = 2; Do[Print[k]; k *= Mod[Plus @@ IntegerDigits[k], 9], {n, 1, 30}] (* Ryan Propper, Oct 13 2005 *) LinearRecurrence[{0, 28}, {2, 4, 16}, 30] (* Harvey P. Dale, Mar 17 2019 *) PROG (PARI) Vec(2*x*(1+2*x-20*x^2)/(1-28*x^2) + O(x^50)) \\ Colin Barker, May 05 2016 CROSSREFS Cf. A010888, A047892. Sequence in context: A297009 A135249 A318154 * A047892 A275911 A334351 Adjacent sequences: A110362 A110363 A110364 * A110366 A110367 A110368 KEYWORD base,easy,nonn AUTHOR Amarnath Murthy, Jul 24 2005 EXTENSIONS More terms from Ryan Propper, Oct 13 2005 Name clarified by Robert Israel, May 05 2016 STATUS approved

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Last modified May 18 08:45 EDT 2024. Contains 372618 sequences. (Running on oeis4.)