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A157810
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Example of periodic sequence arising from Problem S07 - 4 of Harvard College Mathematical Review.
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3
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2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Let V be the set of primes p for which {(3^n-1)/(2^n-1} such that n is a natural number} is contained in Z(p) contained in Q denote the localization of the integral domain Z at the prime ideal (p); that is, the subring of Q consisting of the rational numbers with denominators prime to p. (a) Characterize the set V. (b) subproblem about Wieferich primes A001220. (c) Show that, for every p and element of V, the map N -> F_p given by n -> phi_p ((3^n-1)/(2^n-1}) is periodic. For example, 5 is an element of V, and the corresponding map N > F_5 is 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, ....
Continued fraction expansion of (7+sqrt(93))/6. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 30 2010]
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LINKS
| Vesselin Dimitrov, Problem S07 - 4 (Corrected). Harvard College Mathematical Review, Vol. 1, No. 2, Fall 2007.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1).
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FORMULA
| a(n)=(1/12)*{4*[(n-1) mod 4]+7*(n mod 4)-2*[(n+1) mod 4]+7*[(n+2) mod 4]}, with n>=1 [From Paolo P. Lava (paoloplava(AT)gmail.com), Mar 17 2009]
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CROSSREFS
| Cf. A001220.
Sequence in context: A090000 A109082 A126303 * A072339 A175548 A038571
Adjacent sequences: A157807 A157808 A157809 * A157811 A157812 A157813
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KEYWORD
| nonn,easy
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 07 2009
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