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 A010900 Pisot sequence E(4,13): a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ). 3
 4, 13, 42, 136, 440, 1424, 4609, 14918, 48285, 156284, 505844, 1637264, 5299328, 17152321, 55516872, 179691313, 581606398, 1882483892, 6093030640, 19721296176, 63831867233, 206604436042, 668716032329, 2164431415224, 7005609443657, 22675037578854 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS According to David Boyd his last use (as of April, 2006) of his Pisot number finding program was to prove that in fact this sequence does not satisfy a linear recurrence. He remarks "This took a couple of years in background on various Sun workstations." - Gene Ward Smith, Apr 11 2006 Satisfies a linear recurrence of order 6 just for n <= 23 (see A274952). - N. J. A. Sloane, Aug 07 2016 REFERENCES Cantor, D. G. "Investigation of T-numbers and E-sequences." In Computers in Number Theory, ed. AOL Atkin and BJ Birch, Acad. Press, NY (1971); pp. 137-140. Cantor, D. G. (1976). On families of Pisot E-sequences. In Annales scientifiques de l'École Normale Supérieure (Vol. 9, No. 2, pp. 283-308). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305 D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993. David Cantor, Investigation of T-numbers and E-sequences, In Computers in Number Theory, ed. A. O. L. Atkin and B. J. Birch, Acad. Press, NY (1971); pp. 137-140. [Annotated scanned copy] C. Pisot, La répartition modulo 1 et les nombres algébriques, Ann. Scuola Norm. Sup. Pisa, 7 (1938), 205-248. FORMULA It is known that this does not satisfy any linear recurrence [Boyd]. MATHEMATICA nxt[{a_, b_}]:={b, Floor[b^2/a+1/2]}; NestList[nxt, {4, 13}, 30][[All, 1]] (* Harvey P. Dale, Jun 24 2018 *) PROG (PARI) pisotE(nmax, a1, a2) = {   a=vector(nmax); a[1]=a1; a[2]=a2;   for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1/2));   a } pisotE(50, 4, 13) \\ Colin Barker, Jul 28 2016 CROSSREFS Cf. A007698, A007699, A010916, A274952. See A008776 for definitions of Pisot sequences. Sequence in context: A010919 A277667 A274952 * A175005 A070031 A082989 Adjacent sequences:  A010897 A010898 A010899 * A010901 A010902 A010903 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 13 12:37 EST 2019. Contains 329968 sequences. (Running on oeis4.)