0,3

a(6) has 233 digits. 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, 6.

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

a(2) = a(1)^3 + a(0)^4 = 1^3 + 1^4 = 2.

a(3) = a(2)^3 + a(1)^4 = 2^3 + 1^4 = 9.

a(4) = a(3)^3 + a(2)^4 = 9^3 + 2^4 = 745.

a(5) = a(4)^3 + a(3)^4 = 745^3 + 9^4 = 413500186.

a(6) = a(5)^2 + a(4)^4 = 413500186^3 + 745^4 = 70701255783138724397185481.

Cf. A000283, A112961, A112969, A114793.

Sequence in context: A023366 A000284 A112961 this_sequence A067691 A062840 A024226

Adjacent sequences: A114950 A114951 A114952 this_sequence A114954 A114955 A114956

easy,nonn

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