A201920 a(n) = 2^n mod 125.

1, 2, 4, 8, 16, 32, 64, 3, 6, 12, 24, 48, 96, 67, 9, 18, 36, 72, 19, 38, 76, 27, 54, 108, 91, 57, 114, 103, 81, 37, 74, 23, 46, 92, 59, 118, 111, 97, 69, 13, 26, 52, 104, 83, 41, 82, 39, 78, 31, 62, 124, 123, 121, 117, 109, 93, 61, 122, 119, 113, 101, 77, 29

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Formula

For n > 50: a(n) = a(n-1) - a(n-50) + a(n-51).

G.f.: (1 + x + 2x^2 + 4x^3 + 8x^4 + 16x^5 + 32x^6 - 61x^7 + 3x^8 + 6x^9 + 12x^10 + 24x^11 + 48x^12 - 29x^13 - 58x^14 + 9x^15 + 18x^16 + 36x^17 - 53x^18 + 19x^19 + 38x^20 - 49x^21 + 27x^22 + 54x^23 - 17x^24 - 34x^25 + 57x^26 - 11x^27 - 22x^28 - 44x^29 + 37x^30 - 51x^31 + 23x^32 + 46x^33 - 33x^34 + 59x^35 - 7x^36 - 14x^37 - 28x^38 - 56x^39 + 13x^40 + 26x^41 + 52x^42 - 21x^43 - 42x^44 + 41x^45 - 43x^46 + 39x^47 - 47x^48 + 31x^49 + 63x^50) / ((1-x)*(1+x^2)*(1 - x^2 + x^4 - x^6 + x^8 - x^10 + x^12 - x^14 + x^16 - x^18 + x^20 - x^22 + x^24 - x^26 + x^28 - x^30 + x^32 - x^34 + x^36 - x^38 + x^40 - x^42 + x^44 - x^46 + x^48)).

Periodic with period 100.

Example

a(7) = 2^7 mod 125 = 3.

Mathematica

PowerMod[2, Range[0, 100], 125] (* Harvey P. Dale, Aug 12 2013 *)

Prog

(PARI) a(n)=lift(Mod(2, 125)^n) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) [Modexp(2, n, 125): n in [0..120]]; // G. C. Greubel, Oct 17 2018
(GAP) a:=List([0..100], n->PowerMod(2, n, 125));; Print(a); # Muniru A Asiru, Jan 27 2019

Crossrefs

Cf. A070402, A070336.

Sequence in context: A128901 A025489 A160686 * A343926 A223700 A036140

Adjacent sequences: A201917 A201918 A201919 * A201921 A201922 A201923

Keyword

nonn,easy

Author

Franz Vrabec, Dec 06 2011

Status

approved