A146364 a(n) = smallest primes whose continued fraction have different period.

2, 5, 7, 17, 19, 31, 41, 43, 73, 89, 103, 139, 151, 179, 191, 193, 211, 241, 271, 331, 337, 379, 409, 421, 433, 463, 487, 491, 521, 541, 571, 601, 619, 631, 673, 739, 751, 769, 823, 919, 929, 937, 1033, 1039, 1051, 1201, 1249, 1291, 1321, 1399, 1439, 1471, 1531, 1579, 1609, 1699, 1747, 1753, 1759

Offset

1,1

Comments

This sequence is sorted A146363.

Links

Robert Israel, Table of n, a(n) for n = 1..1500

Maple

g:= proc(n) local c;
      c:= NumberTheory:-ContinuedFraction((1+sqrt(n))/2);
      nops(Term(c, periodic)[2]);
end proc:
R:= NULL: S:= {}: count:= 0:
p:= 1:
while count < 100 do
  p:= nextprime(p);
  v:= g(p);
  if not member(v, S) then
    R:= R, p; count:= count+1; S:= S union {v};
    if count mod 20 = 0 then printf("%d %d\n", count, p) fi
  fi
od:
R; # Robert Israel, Jun 14 2024

Mathematica

$MaxExtraPrecision = 300; s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[n])/2, 1000]; If[Length[k] < 190, AppendTo[aa, 0], m = 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; AppendTo[aa, m]], {n, 1, 1200}]; Print[aa]; bb = {}; Do[k = 1; yes = 0&&PeimeQ[k]; Do[If[aa[[k]] == n && yes == 0, AppendTo[bb, k]; yes = 1], {k, 1, Length[aa]}], {n, 1, 22}]; Sort[bb] (*Artur Jasinski*)

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360, A146363.

Sequence in context: A019334 A045356 A158526 * A105895 A238699 A068360

Adjacent sequences: A146361 A146362 A146363 * A146365 A146366 A146367

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

More terms from Robert Israel, Jun 14 2024

Status

approved