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, 4. Semiprimes in this sequence include a(n) for n = 3, 6.

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

a(2) = Ceiling[a(0)^(3/2) + a(1)^(3/2)] = Ceiling[1^1.5 + 1^1.5] = 2.

a(3) = Ceiling[a(1)^(3/2) + a(2)^(3/2)] = Ceiling[1^1.5 + 2^1.5] = Ceiling[3.82842712] = 4.

a(4) = Ceiling[2^(3/2) + 4^(3/2)] = Ceiling[10.8284271] = 11.

a(5) = Ceiling[(4^(3/2)) + (11^(3/2))] = Ceiling[44.4828727] = 45.

a(6) = Ceiling[(11^(3/2)) + (45^(3/2))] = Ceiling[338.35205] = 339.

a(7) = Ceiling[(45^(3/2)) + (339^(3/2))] = Ceiling[6543.52112] = 6544.

Cf. A000283, A112961, A112969, A114793.

Sequence in context: A067353 A105996 A107703 this_sequence A134019 A120259 A091240

Adjacent sequences: A114951 A114952 A114953 this_sequence A114955 A114956 A114957

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 21 2006