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A133612
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Unique sequence of digits a(0), a(1), a(2), .. such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n satisfies 2^A(k) == A(k) mod 10^k.
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4
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6, 3, 7, 8, 4, 9, 2, 3, 4, 3, 5, 3, 5, 7, 0, 5, 1, 6, 8, 9, 0, 8, 3, 3, 3, 5, 8, 9, 5, 1, 0, 0, 6, 2, 7, 8, 6, 9, 6, 8, 2, 5, 5, 4, 1, 0, 7, 5, 4, 2, 6, 8, 2, 6, 1, 4, 8, 2, 8, 2, 1, 2, 1, 2, 1, 9, 0, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 10-adic expansion of the iterated exponential 2^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g. For n>9, 2^^n == 2948736 (mod 10^7)
Sequences A133612-A133619 and A144539-A144544 generalize the observation that 7^343 == 343 mod 1000.
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REFERENCES
| 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
| J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8
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EXAMPLE
| 2^36 = 68719476736 == 36 (mod 100), 2^736 == 736 (mod 1000), 2^8736 == 8736 (mod 10000), etc.
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CROSSREFS
| Cf. A133613-A133619 and A144539-A144544.
Sequence in context: A200239 A097676 A125123 * A070392 A115371 A096253
Adjacent sequences: A133609 A133610 A133611 * A133613 A133614 A133615
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KEYWORD
| nonn,base
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AUTHOR
| Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 22 2007 and Dec 22 2008
More terms from J. Luis A. Yebra, Dec 12 2008
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