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 A297996 a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + ... + a(n-1))/a(n-1). 1
 2, 3, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 27, 24, 28, 25, 29, 26, 30, 27, 31, 28, 32, 29, 33, 30, 34, 31, 35, 32, 36, 33, 37, 34, 38, 35 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = A168230(n+1) for n >= 3. From Colin Barker, Jan 29 2018: (Start) G.f.: x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)). a(n) = n/2 for n>2 and even. a(n) = (n+7)/2 for n>2 and odd. a(n) = a(n-1) + a(n-2) - a(n-3) for n>5. (End) MATHEMATICA Nest[Append[#, Total[#]/Last[#]] &, Prime@ Range@ 3, 67] (* Michael De Vlieger, Jan 10 2018 *) LinearRecurrence[{1, 1, -1}, {2, 3, 5, 2, 6}, 70] (* Harvey P. Dale, Dec 31 2021 *) PROG (PARI) lista(nn) = {va = vector(nn); for (n=1, 3, va[n] = prime(n)); for (n=4, nn, va[n] = sum(k=1, n-1, va[k])/va[n-1]; ); va; } \\ Michel Marcus, Jan 10 2018 (PARI) Vec(x*(2 + x - 4*x^3 + 2*x^4) / ((1 - x)^2*(1 + x)) + O(x^100)) \\ Colin Barker, Jan 29 2018 CROSSREFS Cf. A168230. Sequence in context: A125766 A093870 A250445 * A239692 A126833 A138512 Adjacent sequences:  A297993 A297994 A297995 * A297997 A297998 A297999 KEYWORD nonn,easy,less AUTHOR Mateusz Pasternak, Jan 10 2018 EXTENSIONS More terms from Michel Marcus, Jan 10 2018 STATUS approved

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)