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A002380
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a(n) = 3^n reduced modulo 2^n.
(Formerly M2235 N0887)
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22
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0, 1, 1, 3, 1, 19, 25, 11, 161, 227, 681, 1019, 3057, 5075, 15225, 29291, 55105, 34243, 233801, 439259, 269201, 1856179, 3471385, 6219851, 1882337, 5647011, 50495465, 17268667, 186023729, 21200275, 63600825, 1264544299, 3793632897, 7085931395
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history;
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OFFSET
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0,4
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COMMENTS
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n such that a(n+1)=3*a(n) is given by A065554. - Benoit Cloitre, Apr 21 2003
a(n) = (fractional part of (3/2)^n without the decimal point)/5^n = A204544(n) / 5^n. - Michel Lagneau, Jan 25 2012
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REFERENCES
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D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 82.
S. S. Pillai, On Waring's problem, J. Indian Math. Soc., 2 (1936), 16-44.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Zak Seidov and Seiichi Manyama, Table of n, a(n) for n = 0..3322 (first 101 terms from Zak Seidov)
Eric Weisstein's World of Mathematics, Fractional Part
Eric Weisstein's World of Mathematics, Power Fractional Parts
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MAPLE
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a:=n->3^n mod(2^n): seq(a(n), n=0..33); # Zerinvary Lajos, Feb 15 2008
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MATHEMATICA
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Table[ PowerMod[3, n, 2^n], {n, 0, 33}] (* Robert G. Wilson v, Dec 14 2006 *)
Table[ 3^n - 2^n * Floor[ (3/2)^n ], {n, 0, 33} ] (* Fred Daniel Kline, Oct 12 2017 *)
x[n_] := -(1/2) + (3/2)^n + ArcTan[Cot[(3/2)^n Pi]]/Pi;
y[n_] := 3^n - 2^n * x[n];
Array[y, 33] (* Fred Daniel Kline, Dec 21 2017 *)
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PROG
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(PARI) concat([0], vector(55, n, lift(Mod(3, 2^n)^n))) \\ Joerg Arndt, Oct 14 2017
(Haskell)
a002380 n = 3^n `mod` 2^n -- Reinhard Zumkeller, Jul 11 2014
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CROSSREFS
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Cf. A060692, A002379, A000079, A000244.
Cf. k^n mod (k-1)^n: this sequence (k=3), A064629 (k=4), A138589 (k=5), A138649 (k=6), A139786 (k=7), A138973 (k=8), A139733 (k=9).
Sequence in context: A147076 A027537 A192721 * A274075 A038455 A067802
Adjacent sequences: A002377 A002378 A002379 * A002381 A002382 A002383
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Jason Earls, Jul 29 2001
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STATUS
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approved
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