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Search: id:A005054
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| 1, 4, 20, 100, 500, 2500, 12500, 62500, 312500, 1562500, 7812500, 39062500, 195312500, 976562500, 4882812500, 24414062500, 122070312500, 610351562500, 3051757812500, 15258789062500, 76293945312500
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Length of repeating cycle of the final n+1 digits in Fermat numbers. - Lekraj Beedassy, Robert G. Wilson v and Eric Weisstein, Jul 05 2004
Number of n-digit endings for a power of 2 whose exponent is greater than or equal to n - J. Lowell, jhbubby(AT)avana.net.
For n>=1, a(n) is equal to the number of functions f:{1,2...,n}->{1,2,3,4,5} such that for a fixed x in {1,2,...,n} and a fixed y in {1,2,3,4,5} 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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T. Koshy,"The Ends Of A Fermat Number", pp. 183-4 Journal Recreational Mathematics, vol. 31(3) 2002-3 Baywood NY.
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 458
Eric Weisstein's World of Mathematics, Fermat Number
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FORMULA
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a(n) = phi[5^n]=A000010[A000351(n)].
a(n)=(4*5^n+0^n)/5 (with 0^0=1). E.g.f. (4exp(5x)+1)/5. - Paul Barry (pbarry(AT)wit.ie), Apr 20 2003
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EXAMPLE
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The last two digits of the Fermat numbers are 17,57,37,97,17,57,37,97,17,57,... with a recurrence period of a(1)=4.
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CROSSREFS
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First differences of A000351. Cf. A000215.
Sequence in context: A098225 A073532 A103771 this_sequence A105480 A082761 A076035
Adjacent sequences: A005051 A005052 A005053 this_sequence A005055 A005056 A005057
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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Better definition from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 13 2008
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