0,3

a(11) = 8 is exact [8^(2/3) + 8^(2/3) = 8.00000000]. It is also a fixed point of this sum of 2/3-power mapping, so that a(n) = 8 for all n>8. 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, 3, 5, 7, 8. Semiprimes in this sequence include a(n) for n = 4, 6.

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

Euler transform of length 8 sequence [ 1, 1, 1, 0, 0, -1, 0, -1]. - Michael Somos Aug 31 2006

G.f.: (1-x^6)(1-x^8)/((1-x)(1-x^2)(1-x^3)). - Michael Somos Aug 31 2006

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

a(3) = Ceiling[a(1)^(2/3) + a(2)^(2/3)] = Ceiling[1^(2/3) + 2^(2/3)] = Ceiling[2.58740105] = 3.

a(4) = Ceiling[2^(2/3) + 3^(2/3)] = Ceiling[3.66748488] = 4.

a(5) = Ceiling[3^(2/3) + 4^(2/3)] = Ceiling[4.59992592] = 5.

a(6) = Ceiling[4^(2/3) + 5^(2/3)] = Ceiling[5.44385984] = 6.

a(7) = Ceiling[5^(2/3) + 6^(2/3)] = Ceiling[6.22594499] = 7.

a(8) = Ceiling[6^(2/3) + 7^(2/3)] = Ceiling[6.96123296] = 7.

(PARI) {a(n)=if(n<1, n==0, if(n>8, 8, n-(n>7)))} /* Michael Somos Aug 31 2006 */

Cf. A000283, A112961, A112969, A114793.

Sequence in context: A101918 A132125 A102672 this_sequence A060207 A134679 A100721

Adjacent sequences: A114952 A114953 A114954 this_sequence A114956 A114957 A114958

easy,nonn

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