A274951 Pisot sequence E(8,12), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

8, 12, 18, 27, 41, 62, 94, 143, 218, 332, 506, 771, 1175, 1791, 2730, 4161, 6342, 9666, 14732, 22453, 34221, 52157, 79494, 121159, 184662, 281449, 428965, 653799, 996476, 1518761, 2314792, 3528048, 5377210, 8195577, 12491140, 19038144, 29016641, 44225186, 67405013, 102734125, 156580349

Offset

0,1

Links

Chai Wah Wu, Table of n, a(n) for n = 0..1000

Maple

f:=proc(n, x, y, r) option remember;
if n=0 then x
elif n=1 then y
else floor(f(n-1, x, y, r)^2/f(n-2, x, y, r) + r); fi; end;
[seq(f(n, 8, 12, 1/2), n=0..60)];

Prog

(Python)
a, b = 8, 12
A274951_list = [a, b]
for i in range(1000):
    c, d = divmod(b**2, a)
    a, b = b, c + (0 if 2*d < a else 1)
    A274951_list.append(b) # Chai Wah Wu, Aug 06 2016

Crossrefs

Cf. A008776, A010916.

Sequence in context: A276403 A171241 A120137 * A364776 A379033 A033477

Adjacent sequences: A274948 A274949 A274950 * A274952 A274953 A274954

Keyword

nonn

Author

N. J. A. Sloane, Aug 05 2016

Status

approved