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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). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A168060 A306076 A069124 * A067769 A066089 A203235

Adjacent sequences:  A218025 A218026 A218027 * A218029 A218030 A218031

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 22 2012

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)