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

0,2

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A350399.

Sequence in context: A061258 A057660 A130972 * A344483 A151923 A187264

Adjacent sequences: A350397 A350398 A350399 * A350401 A350402 A350403

Keyword

nonn

Author

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

Status

approved