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A269266 a(n) = 2^n mod 31.

%I A269266 #59 Sep 08 2022 08:46:15
%S A269266 1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,
%T A269266 2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,
%U A269266 4,8,16,1,2,4,8,16,1,2,4,8,16,1,2,4,8,16,1
%N A269266 a(n) = 2^n mod 31.
%D A269266 Continued fraction expansion of (1651+sqrt(3236405))/2386. - _Bruno Berselli_, Mar 31 2016
%H A269266 Muniru A Asiru, <a href="/A269266/b269266.txt">Table of n, a(n) for n = 0..1000</a>
%H A269266 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F A269266 G.f.: (1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4)/(1 - x^5).
%F A269266 a(n) = a(n-5).
%F A269266 a(n) = 2^(n mod 5). - _Bruno Berselli_, Mar 31 2016
%t A269266 PowerMod[2, Range[0, 100], 31]
%o A269266 (Magma) [Modexp(2, n, 31): n in [0..100]];
%o A269266 (Magma) &cat [[1,2,4,8,16]^^20] // _Bruno Berselli_, Mar 31 2016
%o A269266 (PARI) a(n)=2^(n%5) \\ _Charles R Greathouse IV_, Mar 31 2016
%o A269266 (PARI) x='x+O('x^99); Vec((1+2*x+4*x^2+8*x^3+16*x^4)/(1-x^5)) \\ _Altug Alkan_, Mar 31 2016
%o A269266 (Sage) [2^mod(n,5) for n in (0..100)] # _Bruno Berselli_, Mar 31 2016
%o A269266 (Python) for n in range(0,100):print(2**n%31) # _Soumil Mandal_, Apr 03 2016
%o A269266 (Python) def A269266(n): return pow(2,n,31) # _Chai Wah Wu_, Jan 03 2022
%o A269266 (GAP) List([0..70],n->PowerMod(2,n,31)); # _Muniru A Asiru_, Jan 30 2019
%Y A269266 Cf. A201912 (11th row of the triangle).
%Y A269266 Cf. similar sequences of the type 2^n mod p, where p is a prime: A000034 (p=3), A070402 (p=5), A069705 (p=7), A036117 (p=11), A036118 (p=13), A062116 (p=17), A036120 (p=19), A070335 (p=23), A036122 (p=29), this sequence (p=31), A036124 (p=37), A070348 (p=41), A070349 (p=43), A070351 (p=47), A036128 (p=53), A036129 (p=59), A036130 (p=61), A036131 (p=67).
%K A269266 nonn,easy
%O A269266 0,2
%A A269266 _Vincenzo Librandi_, Mar 31 2016