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 A086088 Limit of ratio of consecutive terms in the tetranacci sequence A000078. 9
 1, 9, 2, 7, 5, 6, 1, 9, 7, 5, 4, 8, 2, 9, 2, 5, 3, 0, 4, 2, 6, 1, 9, 0, 5, 8, 6, 1, 7, 3, 6, 6, 2, 2, 1, 6, 8, 6, 9, 8, 5, 5, 4, 2, 5, 5, 1, 6, 3, 3, 8, 4, 7, 2, 7, 1, 4, 6, 6, 4, 7, 0, 3, 8, 0, 0, 9, 6, 6, 6, 0, 6, 2, 2, 9, 7, 8, 1, 5, 5, 5, 9, 1, 4, 9, 8, 1, 8, 2, 5, 3, 4, 6, 1, 8, 9, 0, 6, 5, 3, 2, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The tetranacci constant corresponds to the Golden Section in a quadripartite division 1 = u_1 + u_2 + u_3 + u_4 of a unit line segment, i.e., if 1/u_1 = u_1/u_2 = u_2/u_3 = u_3/u_4 = c, c is the tetranacci constant. - Seppo Mustonen, Apr 19 2005 The other 3 polynomial roots of 1+x+x^2+x^3-x^4 are -0.77480411321543385... and the complex-conjugated pair -0.07637893113374572508475 +- i * 0.814703647170386526841... - R. J. Mathar, Oct 25 2008 The continued fraction expansion starts 1, 1, 12, 1, 4, 7, 1, 21, 1, 2, 1, 4, 6, 1, 10, 1, 2, 2, 1, 7, 1, 1,... - R. J. Mathar, Mar 09 2012 For n>=4, round(c^prime(n)) == 1 (mod 2*prime(n)). Proof in Shevelev link. - Vladimir Shevelev, Mar 21 2014 REFERENCES O. Deveci, Y. Akuzum, E. Karaduman, O. Erdag, The Cyclic Groups via Bezout Matrices, Journal of Mathematics Research, Vol. 7, No. 2, 2015, pp. 34-41. LINKS S. Litsyn and V. Shevelev, Irrational Factors Satisfying the Little Fermat Theorem, International Journal of Number Theory, vol.1, no.4 (2005), 499-512. V. Shevelev, A property of n-bonacci constant, Seqfan (Mar 23 2014) Eric Weisstein's World of Mathematics, Tetranacci Number Eric Weisstein's World of Mathematics, Disk Covering Problem Eric Weisstein's World of Mathematics, Tetranacci Constant Eric Weisstein's World of Mathematics, Fibonacci n-Step Number EXAMPLE 1.927561975... MATHEMATICA RealDigits[Root[ -1-#1-#1^2-#1^3+#1^4&, 2], 10, 110][[1]] PROG (PARI) real(polroots(1+x+x^2+x^3-x^4)[2]) \\ Charles R Greathouse IV, Jul 19 2012 (PARI) polrootsreal(1+x+x^2+x^3-x^4)[2] \\ Charles R Greathouse IV, Apr 14 2014 CROSSREFS Cf. A000078. Sequence in context: A234371 A172423 A104696 * A231986 A203126 A111506 Adjacent sequences:  A086085 A086086 A086087 * A086089 A086090 A086091 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jul 08 2003 STATUS approved

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Last modified October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)