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A018923 Define the generalized Pisot sequence T(a(0),a(1)) by: a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n). This is T(16,32). 1
16, 32, 63, 124, 244, 480, 944, 1856, 3649, 7174, 14104, 27728, 54512, 107168, 210687, 414200, 814296, 1600864, 3147216, 6187264, 12163841, 23913482, 47012668, 92424472, 181701728, 357216192, 702268543, 1380623604, 2714234540, 5336044608, 10490387488 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Not to be confused with the Pisot T(16,32) sequence, which is essentially A000079. - R. J. Mathar, Feb 13 2016
LINKS
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.
FORMULA
Empirical G.f.: -(8*x^5+4*x^4+2*x^3+x^2-16) / ((x-1)*(x^5+x^4+x^3+x^2+x-1)). - Colin Barker, Dec 21 2012
a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016
MATHEMATICA
T[a_, b_, n_] := Block[{s = {a, b}, k}, Do[k = 2 Last@ s; While[k/s[[i - 1]] >= s[[i - 1]]/s[[i - 2]], k--]; AppendTo[s, k], {i, 3, n}]; s]; T[16, 32, 23] (* or *)
a = {16, 32}; Do[AppendTo[a, Ceiling[a[[n - 1]]^2/a[[n - 2]]] - 1], {n, 3, 23}]; a (* Michael De Vlieger, Feb 15 2016 *)
RecurrenceTable[{a[1] == 16, a[2] == 32, a[n] == Ceiling[a[n-1]^2/a[n-2] - 1]}, a, {n, 40}] (* Vincenzo Librandi, Feb 17 2016 *)
PROG
(PARI) T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a
T(16, 32, 30) \\ Colin Barker, Feb 16 2016
CROSSREFS
Is this the same sequence as A001949?
Sequence in context: A255994 A204645 A236323 * A264901 A339840 A172418
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified May 26 05:37 EDT 2024. Contains 372807 sequences. (Running on oeis4.)