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A020744
Pisot sequences P(8,10), T(8,10).
2
8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138
OFFSET
0,1
COMMENTS
Conjecturally, even sums of four primes. - Charles R Greathouse IV, Feb 16 2012
FORMULA
a(n) = 2*n + 8.
a(n) = 2*a(n-1) - a(n-2).
From Elmo R. Oliveira, Oct 30 2024: (Start)
G.f.: 2*(4 - 3*x)/(1 - x)^2.
E.g.f.: 2*(4 + x)*exp(x).
a(n) = 2*A020705(n) = A028563(n+1) - A028563(n). (End)
MATHEMATICA
LinearRecurrence[{2, -1}, {8, 10}, 70] (* Harvey P. Dale, Jul 19 2015 *)
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[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 *)
PROG
(PARI) a(n)=2*n+8 \\ Charles R Greathouse IV, Feb 16 2012
(PARI) pisotP(nmax, a1, a2) = {
a=vector(nmax); a[1]=a1; a[2]=a2;
for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]-1/2));
a
}
pisotP(50, 8, 10) \\ Colin Barker, Aug 08 2016
CROSSREFS
Subsequence of A005843, A020739. See A008776 for definitions of Pisot sequences.
Sequence in context: A033872 A080752 A262159 * A356657 A008557 A378174
KEYWORD
nonn,easy
STATUS
approved