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 A114950 A quartic quadratic recurrence. 0
 1, 1, 2, 17, 83525, 48670514501156640914, 5611303368570568119463158581109807779153712597124269146443734128560476495542441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(6) has 315 digits. This sequence is related to: A112969 "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) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. Primes in this sequence include a(n) for n = 2, 3. Semiprimes in this sequence include a(n) for n = 5. LINKS FORMULA a(0) = a(1) = 1, for n>1 a(n) = a(n-1)^4 + a(n-2)^2. a(n) ~ c^(4^n), where c = 1.045263645117629170027922399491730015846213509999461317320720034161754262379... . - Vaclav Kotesovec, Dec 18 2014 EXAMPLE a(2) = a(1)^4 + a(0)^2 = 1^4 + 1^2 = 2. a(3) = a(2)^4 + a(1)^2 = 2^4 + 1^2 = 17. a(4) = a(3)^4 + a(2)^2 = 17^4 + 2^2 = 83525. a(5) = a(4)^4 + a(3)^2 = 83525^4 + 17^2 = 48670514501156640914. MATHEMATICA RecurrenceTable[{a ==1, a == 1, a[n] == a[n-1]^4 + a[n-2]^2}, a, {n, 0, 8}] (* Vaclav Kotesovec, Dec 18 2014 *) CROSSREFS Cf. A000283, A112969, A114793. Sequence in context: A078624 A163319 A269836 * A112969 A208208 A290189 Adjacent sequences:  A114947 A114948 A114949 * A114951 A114952 A114953 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Feb 21 2006 EXTENSIONS Formula corrected by Vaclav Kotesovec, Dec 18 2014 Missing a(3) added from Vaclav Kotesovec, Dec 18 2014 STATUS approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)