A002380 a(n) = 3^n reduced modulo 2^n. (Formerly M2235 N0887)

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

Offset

0,4

Comments

A065554 lists the indices n such that a(n+1) = 3*a(n). - 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

References

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).

Links

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.

Maple

a:=n->3^n mod(2^n): seq(a(n), n=0..33); # Zerinvary Lajos, Feb 15 2008

Mathematica

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 *)

Prog

(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

Crossrefs

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: A027537 A192721 A370949 * A274075 A038455 A343890

Adjacent sequences: A002377 A002378 A002379 * A002381 A002382 A002383

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jason Earls, Jul 29 2001

Status

approved