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

1,1

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

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

Crossrefs

Cf. A017077, A007519.

Sequence in context: A306076 A069124 A371810 * A067769 A066089 A203235

Adjacent sequences: A218025 A218026 A218027 * A218029 A218030 A218031

Keyword

nonn

Author

Michel Lagneau, Oct 22 2012

Status

approved