This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002380 M2235 N0887 #78 Feb 16 2025 08:32:25
%S A002380 0,1,1,3,1,19,25,11,161,227,681,1019,3057,5075,15225,29291,55105,
%T A002380 34243,233801,439259,269201,1856179,3471385,6219851,1882337,5647011,
%U A002380 50495465,17268667,186023729,21200275,63600825,1264544299,3793632897,7085931395
%N A002380 a(n) = 3^n reduced modulo 2^n.
%C A002380 A065554 lists the indices n such that a(n+1) = 3*a(n). - _Benoit Cloitre_, Apr 21 2003
%C A002380 a(n) = (fractional part of (3/2)^n without the decimal point)/5^n = A204544(n) / 5^n. - _Michel Lagneau_, Jan 25 2012
%D A002380 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 82.
%D A002380 S. S. Pillai, On Waring's problem, J. Indian Math. Soc., 2 (1936), 16-44.
%D A002380 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002380 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002380 Seiichi Manyama, <a href="/A002380/b002380.txt">Table of n, a(n) for n = 0..3322</a> (first 101 terms from Zak Seidov)
%H A002380 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FractionalPart.html">Fractional Part</a>.
%H A002380 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerFractionalParts.html">Power Fractional Parts</a>.
%p A002380 a:=n->3^n mod(2^n): seq(a(n), n=0..33); # _Zerinvary Lajos_, Feb 15 2008
%t A002380 Table[ PowerMod[3, n, 2^n], {n, 0, 33}] (* _Robert G. Wilson v_, Dec 14 2006 *)
%t A002380 Table[ 3^n - 2^n * Floor[ (3/2)^n ], {n,0,33} ] (* _Fred Daniel Kline_, Oct 12 2017 *)
%t A002380 x[n_] := -(1/2) + (3/2)^n + ArcTan[Cot[(3/2)^n Pi]]/Pi;
%t A002380 y[n_] := 3^n - 2^n * x[n];
%t A002380 Array[y, 33] (* _Fred Daniel Kline_, Dec 21 2017 *)
%o A002380 (PARI) concat([0],vector(55,n,lift(Mod(3,2^n)^n))) \\ _Joerg Arndt_, Oct 14 2017
%o A002380 (Haskell)
%o A002380 a002380 n = 3^n `mod` 2^n -- _Reinhard Zumkeller_, Jul 11 2014
%Y A002380 Cf. A060692, A002379, A000079, A000244.
%Y A002380 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).
%K A002380 nonn,easy
%O A002380 0,4
%A A002380 _N. J. A. Sloane_
%E A002380 More terms from _Jason Earls_, Jul 29 2001