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Search: id:A055272
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| 1, 6, 42, 294, 2058, 14406, 100842, 705894, 4941258, 34588806, 242121642, 1694851494, 11863960458, 83047723206, 581334062442, 4069338437094, 28485369059658, 199397583417606, 1395783083923242, 9770481587462694
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partial sum of A055270.
Conjecture in "Introduction a la theorie des nombres" by d'Armel Mercier and J. M. Deconinck: this is the period length of the fraction 1/7^n. For example 1/7^2=0.0204081632653061224489795918367346938775510204....with a period of 42 digits =6*7=a(2). The period of 1/7^3 has exactly 294=a(3) digits. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2002
Also phi(7^n), where phi is Euler's totient function. - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006
For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5,6,7} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5,6,7} we have f(x)<>y. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 27 2007
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pps. 194-196.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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a(n)=6*7^(n-1), a(0)=1.
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EXAMPLE
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a(n)=7a(n-1)+[(-1)^n]*C(1,1-n). G.f.(x)=(1-x)/(1-7x).
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MATHEMATICA
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Table[EulerPhi[7^n], {n, 0, 19}] - Alonso Delarte (alonso.delarte(AT)gmail.com), May 08 2006
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CROSSREFS
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Cf. A000420 and A055270.
Sequence in context: A057089 A110711 A156361 this_sequence A155196 A147838 A127628
Adjacent sequences: A055269 A055270 A055271 this_sequence A055273 A055274 A055275
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, May 28 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 30 2000
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