A391136 Primes p == 9 (mod 16) for which the real part of the octonic Gauss sum ("normalized", i.e., divided by sqrt(p) ) is less than 1.

41, 137, 233, 281, 617, 761, 809, 953, 1033, 1433, 1657, 1753, 1913, 1993, 2089, 2137, 2153, 2441, 2473, 2617, 2633, 2713, 2729, 2777, 3049, 3209, 3881, 4217, 4457, 4649, 4729, 4793, 4889, 4937, 5113, 5417, 5641, 5689, 5801, 5849, 5881, 6089, 6121, 6217, 6553, 6569, 6857

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. A387776, A391135, A390758, A390759.

Sequence in context: A013643 A142333 A028343 * A165816 A325069 A321890

Adjacent sequences: A391133 A391134 A391135 * A391137 A391138 A391139

Keyword

nonn

Author

Zoltan Reti, Nov 30 2025

Status

approved