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Pisot sequences P(8,10), T(8,10).
1

%I #24 Jun 20 2024 11:48:09

%S 8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,

%T 54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,

%U 100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138

%N Pisot sequences P(8,10), T(8,10).

%C Conjecturally, even sums of four primes. - _Charles R Greathouse IV_, Feb 16 2012

%H Colin Barker, <a href="/A020744/b020744.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2n+8. a(n) = 2a(n-1) - a(n-2).

%t LinearRecurrence[{2,-1},{8,10},70] (* _Harvey P. Dale_, Jul 19 2015 *)

%t P[x_, y_, z_] := Block[{a}, a[0] = x; a[1] = y; a[n_] := a[n] = Ceiling[a[n - 1]^2/a[n - 2] - 1/2]; Table[a[n], {n, 0, z}]]; P[8, 10, 65] (* or *)

%t T[x_, y_, z_] := Block[{a}, a[0] = x; a[1] = y; a[n_] := a[n] = Floor[a[n - 1]^2/a[n - 2]]; Table[a[n], {n, 0, z}]]; T[8, 10, 65] (* _Michael De Vlieger_, Aug 08 2016 *)

%o (PARI) a(n)=2*n+8 \\ _Charles R Greathouse IV_, Feb 16 2012

%o (PARI) pisotP(nmax, a1, a2) = {

%o a=vector(nmax); a[1]=a1; a[2]=a2;

%o for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));

%o a

%o }

%o pisotP(50, 8, 10) \\ _Colin Barker_, Aug 08 2016

%Y Subsequence of A005843, A020739. See A008776 for definitions of Pisot sequences.

%K nonn,easy

%O 0,1

%A _David W. Wilson_