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

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, 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, 4, 8, 16, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 1, 2, 4, 8, 16, 1

Offset: 0

Author

Vincenzo Librandi, Mar 31 2016

Keywords

• nonn
• easy

References

• Continued fraction expansion of (1651+sqrt(3236405))/2386. - Bruno Berselli, Mar 31 2016

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Crossrefs

Cf. A201912 (11th row of the triangle).

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).

Programs

GAP

List([0..70],n->PowerMod(2,n,31)); # Muniru A Asiru, Jan 30 2019

Magma

[Modexp(2, n, 31): n in [0..100]];

Magma

&cat [[1,2,4,8,16]^^20] // Bruno Berselli, Mar 31 2016

Mathematica

PowerMod[2, Range[0, 100], 31]

PARI

a(n)=2^(n%5) \\ Charles R Greathouse IV, Mar 31 2016

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

Python

for n in range(0,100):print(2**n%31) # Soumil Mandal, Apr 03 2016

Python

def A269266(n): return pow(2,n,31) # Chai Wah Wu, Jan 03 2022

Sage

[2^mod(n,5) for n in (0..100)] # Bruno Berselli, Mar 31 2016

Formula

G.f.: (1 + 2*x + 4*x^2 + 8*x^3 + 16*x^4)/(1 - x^5).

a(n) = a(n-5).

a(n) = 2^(n mod 5). - Bruno Berselli, Mar 31 2016