A351297 a(n) is the least number k such that (6*i+2)*k^2-1 is prime for i = 0..n-1 but not for i = n.

6, 2, 4, 21, 1970, 1732325, 304915555

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Example

a(4) = 21 because 2*21^2-1 = 881, 8*21^2-1 = 3527, 14*21^2-1 = 6173, and 20*21^2-1 = 8819 are prime but 26*21^2-1 = 11465 is not, and 21 is the least number that works.

Maple

W:= Vector(6): count:= 0:
f:= proc(p) local i;
     for i from 0 do
       if not isprime((2+6*i)*p^2-1) then return i fi;
     od
end proc:
for x from 1 while count < 6 do
  v:= f(x);
  if v > 0 and W[v] = 0 then W[v]:= x; count:= count+1;  fi;
od:
convert(W, list);

Mathematica

f[k_] := Module[{i = 0}, While[PrimeQ[(6*i + 2)*k^2 - 1], i++]; i]; seq[m_, nmax_] := Module[{s = Table[0, {m}], n = 1, c = 0, i}, While[c < m && n < nmax, i = f[n]; If[i > 0 && i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; TakeWhile[s, # > 0 &]]; seq[6, 10^7] (* Amiram Eldar, Feb 06 2022 *)

Crossrefs

Sequence in context: A329591 A123139 A027599 * A248272 A058160 A033939

Adjacent sequences: A351294 A351295 A351296 * A351298 A351299 A351300

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Feb 06 2022

Extensions

a(7) from Amiram Eldar, Feb 06 2022

Status

approved