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 A225159 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 7/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. 1
 1, 6, 43, 2143, 5211907, 30351298460743, 1016966398053911225889737707, 1130815308619683511655208290917557601522304473342184143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numerators of the sequence of fractions f(n) is A165425(n+1), hence sum(A165425(i+1)/a(i),i=1..n) = product(A165425(i+1)/a(i),i=1..n) = A165425(n+2)/A225166(n). LINKS FORMULA a(n) = 7^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1. a(n) = 7^(2^(n-2)) - p(n) with a(1) = 1 and p(n) = p(n-1)*a(n-1) with p(1) = 1. EXAMPLE f(n) = 7, 7/6, 49/43, 2401/2143, ... 7 + 7/6 = 7 * 7/6 = 49/6; 7 + 7/6 + 49/43 = 7 * 7/6 * 49/43 = 2401/258; ... MAPLE b:=n->7^(2^(n-2)); # n > 1 b(1):=7; p:=proc(n) option remember; p(n-1)*a(n-1); end; p(1):=1; a:=proc(n) option remember; b(n)-p(n); end; a(1):=1; seq(a(i), i=1..9); CROSSREFS Cf. A100441, A165425, A225166. Sequence in context: A159604 A090338 A090339 * A078810 A114074 A075337 Adjacent sequences:  A225156 A225157 A225158 * A225160 A225161 A225162 KEYWORD nonn AUTHOR Martin Renner, Apr 30 2013 STATUS approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)