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 A178255 Decimal expansion of (3+sqrt(17))/2. 5
 3, 5, 6, 1, 5, 5, 2, 8, 1, 2, 8, 0, 8, 8, 3, 0, 2, 7, 4, 9, 1, 0, 7, 0, 4, 9, 2, 7, 9, 8, 7, 0, 3, 8, 5, 1, 2, 5, 7, 3, 5, 9, 9, 6, 1, 2, 6, 8, 6, 8, 1, 0, 2, 1, 7, 1, 9, 9, 3, 1, 6, 7, 8, 6, 5, 4, 7, 4, 7, 7, 1, 7, 3, 1, 6, 8, 8, 1, 0, 7, 9, 6, 7, 9, 3, 9, 3, 1, 8, 2, 5, 4, 0, 5, 3, 4, 2, 1, 4, 8, 3, 4, 2, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Continued fraction expansion of (3+sqrt(17))/2 is A109007. a(n) = A082486(n) for n > 1. The rectangle R whose shape (i.e., length/width) is (3+sqrt(17))/2 can be partitioned into rectangles of shapes 3 and 3/2 in a manner that matches the periodic continued fraction [3, 3/2, 3, 3/2, ...].  R can also be partitioned into squares so as to match the periodic continued fraction [3, 1, 1, 3, 1, 1,...].  For details, see A188635. - Clark Kimberling, May 07 2011 LINKS EXAMPLE (3+sqrt(17))/2 = 3.56155281280883027491... MATHEMATICA FromContinuedFraction[{3, 3/2, {3, 3/2}}] ContinuedFraction[%, 100] (* [3, 1, 1, 3, 1, 1, ...] *) RealDigits[N[%%, 120]]    (* A178255 *) N[%%%, 40] (* from Clark Kimberling, May 07 2011 *) CROSSREFS Cf. A082486 (decimal expansion of (5+sqrt(17))/2), A010473 (decimal expansion of sqrt(17)), A109007 (repeat 3, 1, 1). Sequence in context: A111950 A274792 A243589 * A154467 A152713 A218802 Adjacent sequences:  A178252 A178253 A178254 * A178256 A178257 A178258 KEYWORD cons,nonn AUTHOR Klaus Brockhaus, May 24 2010 STATUS approved

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