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Search: id:A157810
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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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1
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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; listen)
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OFFSET
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1,1
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COMMENT
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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, ....
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LINKS
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Vesselin Dimitrov, Problem S07 - 4 (Corrected). Harvard College Mathematical Review, Vol. 1, No. 2, Fall 2007.
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FORMULA
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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 (ppl(AT)spl.at), Mar 17 2009]
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CROSSREFS
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Cf. A001220.
Sequence in context: A090000 A109082 A126303 this_sequence A072339 A038571 A008687
Adjacent sequences: A157807 A157808 A157809 this_sequence A157811 A157812 A157813
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 07 2009
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