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 A225157 Denominators of the sequence of fractions f(n) defined recursively by f(1) = 5/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. 2
 1, 4, 21, 541, 345181, 136901485261, 21135572172649245550621, 496712610012943408146407697714437299262548141, 271328559212953102170688304392824035451911661168940831351173011072850527195615099225368381 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numerators of the sequence of fractions f(n) is A165423(n+1), hence sum(A165423(i+1)/a(i),i=1..n) = product(A165423(i+1)/a(i),i=1..n) = A165423(n+2)/A225164(n) = A176594(n-1)/A225164(n). LINKS Table of n, a(n) for n=1..9. FORMULA a(n) = 5^(2^(n-2)) - product(a(i),i=1..n-1), n > 1 and a(1) = 1. a(n) = 5^(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) = 5, 5/4, 25/21, 625/541, ... 5 + 5/4 = 5 * 5/4 = 25/4; 5 + 5/4 + 25/21 = 5 * 5/4 * 25/21 = 625/84; ... MAPLE b:=n->5^(2^(n-2)); # n > 1 b(1):=5; 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, A165423, A176594, A225164. Sequence in context: A270586 A048164 A118909 * A158947 A000868 A000875 Adjacent sequences: A225154 A225155 A225156 * A225158 A225159 A225160 KEYWORD nonn,frac AUTHOR Martin Renner, Apr 30 2013 STATUS approved

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Last modified February 29 11:22 EST 2024. Contains 370425 sequences. (Running on oeis4.)