A350400 a(n) is the least k with A350399(k) = n, or 0 if there is no such k.

1, 3, 7, 11, 21, 24, 30, 60, 42, 45, 63, 75, 90, 135, 147, 198, 165, 105, 252, 264, 180, 399, 513, 375, 270, 210, 330, 405, 654, 255, 315, 345, 465, 480, 570, 555, 390, 1020, 675, 798, 777, 1110, 900, 660, 585, 525, 855, 825, 960, 630, 924, 735, 1419, 1305, 840, 975, 780, 1350, 945, 1050, 1500

Offset: 0

Author

J. M. Bergot and Robert Israel, Dec 28 2021

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n.

Examples

			a(3) = 11 because A350399(11) = 3 and this is the first appearance of 3 in A350399.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A350399.

Programs

Maple

f:= proc(k) local P,i;
  P:= select(t -> isprime(t) and isprime(2*k-t) and isprime(-t^2 mod (2*k)), [2,seq(i,i=3..k,2)]);
  nops(P);
end proc:
N:= 60: # for a(0) to a(N)
V:= Array(0..N): count := 0:
for k from 1 while count < N+1 do
  v:= f(k);
  if v <= N and V[v] = 0 then
    count:= count+1;
    V[v]:= k;
  fi;
od:
convert(V,list);

Mathematica

a[n_] := Count[Select[Range[2, 2*n], PrimeQ], ?(# >= n && PrimeQ[2*n - #] && PrimeQ[Mod[#*(2*n - #), 2*n]] &)]; seq[len, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[n < nmax && c < len, i = a[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; TakeWhile[s, # > 0 &]]; seq[60, 10^4] (* Amiram Eldar, Dec 30 2021 *)