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A206636
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a(n) = 2^^(n+2) modulo 10^n, where ^^ denotes a power tower (see A133612).
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3
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6, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 98615075353432948736, 8098615075353432948736
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OFFSET
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1,1
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COMMENTS
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For all m>n+1, 2^^m == 2^^(n+2) (mod 10^n). Hence, each term represents the trailing decimal digits of 2^^m for every sufficiently large m.
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REFERENCES
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M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6.
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LINKS
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FORMULA
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For n>1, a(n) = 2^a(n-1) mod 10^n.
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MATHEMATICA
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(* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link, then *) $RecursionLimit = 2^14; a[n_] := SuperPowerMod[2, n +2, 10^n]; Array[a, 22] (* Robert G. Wilson v, Apr 20 2020 *)
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CROSSREFS
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Cf. A133612, A113627, A109405, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A183613, A144539, A144540, A144541, A144542, A144543, A144544.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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