A385164 Let p = A002145(n) be the n-th prime == 3 (mod 4); 8*a(n) is the multiplicative order of 1+-i modulo p in Gaussian integers.

1, 3, 5, 9, 11, 5, 7, 23, 29, 33, 35, 39, 41, 51, 53, 7, 65, 69, 15, 81, 83, 89, 95, 99, 105, 37, 113, 119, 25, 131, 135, 47, 51, 155, 15, 173, 179, 183, 189, 191, 209, 43, 73, 221, 231, 233, 239, 243, 245, 83, 251, 261, 273, 281, 57, 293, 299, 303, 309, 45, 107, 323, 329, 11, 115

Offset: 1

Author

Jianing Song, Jun 20 2025

Keywords

• nonn
• easy

Examples

			For A002145(4) = 19: Since (1+i)^(4k) = (-4)^k, we have (1+i)^72 == 1 (mod 19), and 72 is the smallest such exponent. Hence a(4) = 72/8 = 9.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002145, A385163.

Programs

PARI

forprime(p=3, 1e3, if(p%4==3, print1(znorder(Mod(-4,p))/2, ", ")))

Formula

a(n) = ord(-4,p)/2, where ord(a,p) is the multiplicative order of a modulo p.