A377882 - OEIS

%I #11 Nov 12 2024 22:19:21

%S 2,3,9,11,29,75,77,101,105,107,221,225,235,257,315,321,323,357,363,

%T 389,411,417,431,453,455,461,501,509,515,519,557,635,645,655,689,795,

%U 799,851,885,887,911,915,921,923,933,977,989,1029,1033,1037,1071,1073,1145,1167,1175,1187,1197,1201,1241

%N Numbers i for which A194627(i) is prime.

%H Robert Israel, <a href="/A377882/b377882.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%p v:= 1: p:= 0: q:= 0: np:= 0: R:= NULL:

%p for i from 1 while np < 100 do

%p   if isprime(v) then p:= p+1; R:= R, i; np:= np+1 else q:= q+1 fi;

%p   v:= p^2 + q^2 + 1;

%p od:

%p R;

%t 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 *)

%Y Cf. A194627, A377791.

%K nonn

%O 1,1

%A _Robert Israel_, Nov 10 2024