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A133612 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. +0
3
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; listen)
OFFSET

0,1

COMMENT

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.

REFERENCES

J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), Preprint, Oct 28 2008.

EXAMPLE

2^36 = 68719476736 == 36 (mod 100), 2^736 == 736 (mod 1000), 2^8736 == 8736 (mod 10000), etc.

CROSSREFS

Cf. A133613-A133619 and A144539-A144544.

Sequence in context: A011191 A097676 A125123 this_sequence A070392 A115371 A096253

Adjacent sequences: A133609 A133610 A133611 this_sequence A133613 A133614 A133615

KEYWORD

nonn,base

AUTHOR

Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007

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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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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