A377940 a(n) is the least number k such that the least j > k for which k is a primitive root is also the least j > n + k for which n + k is a primitive root, or -1 if there is no such k.

20, 6, 32, 10, 39, 28, 38, 18, 18, 42, 46, 42, 88, 42, 46, 173, 46, 78, 229, 102, 102, 294, 78, 150, 210, 150, 210, 193, 232, 193, 848, 488, 330, 226, 226, 328, 488, 328, 294, 172, 172, 294, 294, 294, 462, 328, 736, 328, 328, 294, 1098, 328, 328, 1196, 172, 172, 1322, 172, 1196, 856, 1108, 889

Offset

1,1

Comments

a(n) is the least k, if it exists, such that 0 < A377938(k) = A377938(k+n).

Links

Robert Israel, Table of n, a(n) for n = 1..500

Example

a(3) = 32 because A377938(32) = A377938(35) = 37, i.e. 37 is the least number j > 32 such that 32 is a primitive root mod j and the least number j > 35 such that 35 is a primitive root mod j, and no number less than 32 works.

Maple

N:= 10^6:
P:= select(isprime, {seq(i, i=3..N, 2)}):Cands:= map(proc(t) local i; (seq(t^i, i=1..ilog[t](N)), seq(2*t^i, i=1..ilog[t](N/2))) end proc, P):
Cands:= sort(convert({4} union Cands, list)):
nC:= nops(Cands):
Phis:= map(numtheory:-phi, Cands):
f:= proc(n)
option remember;
local k0, k;
      if issqr(n) then return -1 fi;
      k0:= ListTools:-BinaryPlace(Cands, n)+1;
      for k from k0 to nC do
        if igcd(Cands[k], n) = 1 and numtheory:-order(n, Cands[k]) = Phis[k] then return Cands[k] fi
      od;
    FAIL
end proc:
g:= proc(n)
  local k;
  for k from n+1 do
    if f(k) > 0 and f(k) = f(k+n) then return k
  elif f(k) = FAIL and f(k+n) = FAIL then return FAIL fi
  od
end proc:
map(g, [$1..200]);

Crossrefs

Cf. A377938.

Sequence in context: A076594 A174991 A217418 * A370499 A196102 A196099

Adjacent sequences: A377937 A377938 A377939 * A377941 A377942 A377943

Keyword

nonn

Author

Robert Israel, Nov 11 2024

Status

approved