Perrin Sequence

The Integer Sequence defined by the recurrence

(1)

(2)

			(3)
			(4)
			(5)

(6)

(7)

Perrin (1899) investigated the sequence and noticed that if is Prime, then . The first statement of this fact isattributed to É. Lucas in 1876 by Stewart (1996). Perrin also searched for but did not find any Composite Number in the sequence such that . Such numbers are now known as Perrin Pseudoprimes. Malo(1900), Escot (1901), and Jarden (1966) subsequently investigated the series and also found no PerrinPseudoprimes. Adams and Shanks (1982) subsequently found that 271,441 is such a number.

References

Adams, W. and Shanks, D. ``Strong Primality Tests that Are Not Sufficient.'' Math. Comput. 39, 255-300, 1982.

Escot, E.-B. ``Solution to Item 1484.'' L'Intermédiare des Math. 8, 63-64, 1901.

Jarden, D. Recurring Sequences. Jerusalem: Riveon Lematematika, 1966.

Perrin, R. ``Item 1484.'' L'Intermédiare des Math. 6, 76-77, 1899.

Stewart, I. ``Tales of a Neglected Number.'' Sci. Amer. 274, 102-103, June 1996.

Sloane, N. J. A. SequenceA001608/M0429in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

• Riemann P-Differential Equation
• Riemann P-Series
• Riemann-Roch Theorem
• Riemann Series Theorem
• Riemann's Formula
• Riemann-Siegel Functions
• Riemann's Integral Theorem
• Riemann's Moduli Problem
• Riemann's Moduli Space
• Riemann Space
• Riemann Sphere
• Riemann-Stieltjes Integral
• Riemann Sum
• Riemann Surface
• Riemann Tensor
• Riemann Theta Function
• Riemann Weighted Prime-Power Counting Function
• Riemann Xi Function
• Riemann Zeta Function
• Riesel Number
• Riesz-Fischer Theorem
• Riesz Representation Theorem
• Riesz's Theorem
• Riffle Shuffle
• Rigby Points