A365103 Number of distinct quartic residues x^4 (mod 4^n), x=0..4^n-1.

1, 2, 2, 6, 18, 70, 274, 1094, 4370, 17478, 69906, 279622, 1118482, 4473926, 17895698, 71582790, 286331154, 1145324614, 4581298450, 18325193798, 73300775186, 293203100742, 1172812402962, 4691249611846, 18764998447378

Offset: 0

Author

Albert Mukovskiy, Aug 24 2023

Keywords

• nonn

Comments

a(n) = A364811(2n).

For n>=2, A319281(a(n)) == 4^n + [n mod 2 == 1].

For n>=2, a(n)=k: [ A319281(k) == 4^n + [n mod 2 == 1] ].

Links

• Index entries for linear recurrences with constant coefficients, signature (4, 1, -4).

Crossrefs

Cf. A023105, A046631, A195637, A365104, A364811, A319281.

Programs

Mathematica

a[n_] = Ceiling[4^n/15] + Boole[Mod[n,2]==1]; Array[a, 24]

PARI

a(n) = ceil(4^n/15)+(Mod(n,2)==1);

Python

def A365103(n): return len({pow(x,4,1<<(n<<1)) for x in range(1<<(n<<1))}) # Chai Wah Wu, Sep 18 2023

Formula

a(n) = ceiling(4^n/15) + (n mod 2).