A391135 Primes p == 9 (mod 16) for which the real part of the octonic Gauss sum ("normalized", i.e., divided by sqrt(p) ) is greater than 1.

73, 89, 313, 409, 457, 521, 569, 601, 857, 937, 1049, 1097, 1129, 1193, 1289, 1321, 1481, 1609, 1721, 1801, 2281, 2297, 2377, 2393, 2521, 2857, 2953, 2969, 3001, 3257, 3433, 3449, 3529, 3593, 3673, 3769, 3833, 3929, 4057, 4073, 4153, 4201, 4297, 4409, 4441, 4969, 5081

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Mathematica

d = 4;
Select[Prime[Range[1000]], Mod[#, 2^(d)] == 2^(d - 1) + 1 && Sum[Re[Exp[x^(2^(d - 1))*2*Pi*I/#]], {x, 0, # - 1}]/Sqrt[#] > 1 &]

Crossrefs

Cf. A105126, A387776, A391136, A390758, A390759.

Sequence in context: A065111 A325070 A152308 * A382153 A072052 A333391

Adjacent sequences: A391132 A391133 A391134 * A391136 A391137 A391138

Keyword

nonn

Author

Zoltan Reti, Nov 30 2025

Status

approved