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 A133613 Decimal digits such that for all k>=1, the number A(k) := Sum_{n = 0..k-1 } a(n)*10^n satisfies the congruence 3^A(k) == A(k) (mod 10^k). 17
 7, 8, 3, 5, 9, 1, 4, 6, 4, 2, 6, 2, 7, 2, 6, 5, 7, 5, 4, 0, 1, 9, 5, 0, 9, 3, 4, 6, 8, 1, 5, 8, 4, 8, 1, 0, 7, 6, 9, 3, 2, 7, 8, 4, 3, 2, 2, 2, 3, 0, 0, 8, 3, 6, 6, 9, 4, 5, 0, 9, 7, 6, 9, 3, 9, 9, 8, 1, 6, 9, 9, 3, 6, 9, 7, 5, 3, 5, 2, 6, 5, 1, 5, 8, 3, 9, 1, 8, 1, 0, 5, 6, 2, 8, 4, 2, 4, 0, 4, 9, 8, 0, 5, 1, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 10-adic expansion of the iterated exponential 3^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n>9, 3^^n == 4195387 (mod 10^7). This sequence also gives many final digits of Graham's number ...399618993967905496638003222348723967018485186439059104575627262464195387. - Paul Muljadi, Sep 08 2008 and J. Luis A. Yebra, Dec 22 2008 Graham's number is usually defined as 3^^64 [see M. Gardner and Wikipedia], in which case only its 62 lowermost digits are guaranteed to match this sequence. To avoid such confusion, it would be best to interpret this sequence as a real-valued constant 0.783591464..., corresponding to 3^^k in the limit of k->infinity, and call it Graham's constant G(3). Generalizations to G(n) and G(n,base) are obvious. - Stanislav Sykora, Nov 07 2015 REFERENCES M. Gardner, Mathematical Games, Scientific American 237, 18 - 28 (1977). M. RipĂ , La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 11-12, 69-78. ISBN 978-88-6178-789-6. Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229. LINKS Robert G. Wilson v, Table of n, a(n) for n = 0..10039 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. Robert P. Munafo, Large Numbers [From Robert G. Wilson v, May 07 2010] Reddit user atticdoor, Spotted an error in the comments of sequence A133613. Wikipedia, Graham's number FORMULA a(n) = floor( A183613(n+1) / 10^n ). EXAMPLE 783591464262726575401950934681584810769327843222300836694509769399816993697535... Consider the sequence 3^^n: 1, 3, 27, 7625597484987, ... From 3^^3 = 7625597484987 onwards, all terms end with the digits 87. This follows from Euler's generalization of Fermat's little theorem. MATHEMATICA (* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) \$RecursionLimit = 2^14; f[n_] := SuperPowerMod[3, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *) CROSSREFS Cf. A133612, A133614, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544. Sequence in context: A020843 A241296 A083648 * A296140 A194622 A193010 Adjacent sequences:  A133610 A133611 A133612 * A133614 A133615 A133616 KEYWORD nonn,base AUTHOR Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007 EXTENSIONS More terms from J. Luis A. Yebra, Dec 12 2008 Edited by N. J. A. Sloane, Dec 22 2008 More terms from Robert G. Wilson v, May 07 2010 STATUS approved

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Last modified October 19 00:36 EDT 2018. Contains 316327 sequences. (Running on oeis4.)