A377882 Numbers i for which A194627(i) is prime.

2, 3, 9, 11, 29, 75, 77, 101, 105, 107, 221, 225, 235, 257, 315, 321, 323, 357, 363, 389, 411, 417, 431, 453, 455, 461, 501, 509, 515, 519, 557, 635, 645, 655, 689, 795, 799, 851, 885, 887, 911, 915, 921, 923, 933, 977, 989, 1029, 1033, 1037, 1071, 1073, 1145, 1167, 1175, 1187, 1197, 1201, 1241

Offset: 1

Author

Robert Israel, Nov 10 2024

Keywords

• nonn

Examples

			a(3) = 9 because the third prime in A194627 is A194627(9) = 41.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A194627, A377791.

Programs

Maple

v:= 1: p:= 0: q:= 0: np:= 0: R:= NULL:
for i from 1 while np < 100 do
  if isprime(v) then p:= p+1; R:= R, i; np:= np+1 else q:= q+1 fi;
  v:= p^2 + q^2 + 1;
od:
R;

Mathematica

s={};t= {1};(* t is A194627 *) Do[ps = Count[t, ?(PrimeQ[#] &)];AppendTo[t, ps^2 + (n - ps - 1)^2 + 1];If[PrimeQ[t[[-1]] ],AppendTo[s,n]], {n, 2,1241}]; s (* _James C. McMahon, Nov 12 2024 *)

Formula

A194627(a(n)) = A377791(n).

A377791(n) = (n-1)^2 + (a(n)-n)^2 + 1.