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A365103
Number of distinct quartic residues x^4 (mod 4^n), x=0..4^n-1.
6
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
0,2
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] ].
FORMULA
a(n) = ceiling(4^n/15) + (n mod 2).
MATHEMATICA
a[n_] = Ceiling[4^n/15] + Boole[Mod[n, 2]==1]; Array[a, 24]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Albert Mukovskiy, Aug 24 2023
STATUS
approved