A218028 a(n) is the smallest positive integer k such that k^4 + 1 == 0 mod p, where p is the n-th prime of the form p = 1 + 8*b (see A007519).

2, 3, 10, 12, 33, 18, 10, 9, 12, 8, 4, 60, 5, 85, 70, 45, 31, 79, 92, 170, 43, 76, 152, 59, 59, 139, 256, 64, 62, 40, 44, 188, 177, 18, 14, 156, 227, 192, 231, 223, 79, 31, 75, 362, 7, 239, 338, 402, 6, 235, 114, 72, 342, 511, 15, 483, 310, 355, 104, 292, 232

Offset: 1

Author

Michel Lagneau, Oct 22 2012

Keywords

• nonn

Comments

A007519(n) : primes of form 8n+1.

Examples

			a(5) = 33 because 33^4+1 = 1185922 = 2 * 97 * 6113 with A007519(5) = 97.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 521.

Crossrefs

Cf. A017077, A007519.

Programs

Maple

V:= Vector(100): count:= 0:
for p from 9 by 8 while count < 100 do
  if isprime(p) then
      count:= count+1; V[count]:=min(map(rhs@op,[msolve(k^4+1,p)]))
    fi
od:
convert(V,list); # Robert Israel, Mar 13 2018

Mathematica

aa = {}; Do[p = Prime[n]; If[Mod[p, 8] == 1, k = 1; While[ ! Mod[k^4 + 1, p] == 0, k++ ]; AppendTo[aa, k]], {n, 300}]; aa