0,3

This sequence is related to: A112961 "a cubic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^3 + a(n-2)^3 A112969 "a quartic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^4 + a(n-2)^4, which is the quartic (or biquadratic) analogue of the Fibonacci sequence similarly to A000283 being the quadratic analogue of the Fibonacci sequence. Primes in this sequence include a(n) for n = 2. Semiprimes in this sequence include a(n) for n = 3, 4, 5, 7, 8.

a(0) = a(1) = 1, for n>1 a(n) = Ceiling[a(n-1)^(4/3) + a(n-2)^(4/3)].

a(2) = Ceiling[a(0)^(4/3) + a(1)^(4/3)] = Ceiling[1^(4/3) + 1^(4/3)] = 2.

a(3) = Ceiling[a(1)^(4/3) + a(2)^(4/3)] = Ceiling[1^(4/3) + 2^(4/3)] = Ceiling[3.5198421] = 4.

a(4) = Ceiling[2^(4/3) + 4^(4/3)] = Ceiling[8.86944631] = 9.

a(5) = Ceiling[4^(4/3) + 9^(4/3)] = Ceiling[25.0703586] = 26.

a(6) = Ceiling[9^(4/3) + 26^(4/3)] = Ceiling[95.7456522] = 96.

a(7) = Ceiling[26^(4/3) + 96^(4/3)] = Ceiling[516.595167] = 517.

a(8) = Ceiling[96^(4/3) + 517^(4/3)] = Ceiling[4588.99022] = 4589.

Cf. A000283, A112961, A112969, A114793.

Sequence in context: A125799 A087378 A004252 this_sequence A002773 A112706 A110138

Adjacent sequences: A114954 A114955 A114956 this_sequence A114958 A114959 A114960

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006