0,4

The sequence is rather simple. It becomes more interesting if you apply other periodic correction patterns. What is also interesting that it (and related sequences like 0,1,1,0,1,1,0,1,1,0,...) was used to cryptanalyse RC5 block-cipher since it describes the Hamming weight of a difference if at every 3rd step there is no data rotation. Since the attacker has to pay in probability to cause no rotations, the related question was how many corrected Fibonacci sequences with up to m corrections are there. The paper contains a recursive program that enumerates all "corrected" Fibonacci sequences of length N, with up to m corrections (in that case we do not restrict the locations of the corrections).

0, 1, 1, 2, 3, 5, 2, 7, 9, 16, 7, 23, 30, 53... = Fibonacci with corrections at every 4th step.

A. Biryukov and E. Kushilevitz, "Improved Cryptanalysis of RC5", Advances in Cryptology, Lecture Notes in Computer Science 1403, Proceedings of EUROCRYPT'98, pp. 85 -99, 1998.

A. Biryukov, Home Page

A. Biryukov and E. KushilevitzImproved Cryptanalysis of RC5 Lecture Notes in Computer Science 1403, Proceedings of EUROCRYPT'98, pp. 85-99, 1998.

a(n) = a(n-1) + a(n-2); if n = 3k, n=3k+1, for k=1, 2, 3, .. a(n) = a(n-1) - a(n-2); if n = 3k+2, for k=0, 1, 2, 3, ... a(0) = 0, a(1) = 1;

Adjacent sequences: A092939 A092940 A092941 this_sequence A092943 A092944 A092945

Sequence in context: A104706 A094137 A038802 this_sequence A131225 A137671 A026370

nonn

Alex Biryukov, Apr 19 2004