A264665 - OEIS

%I #20 Nov 25 2015 02:31:34

%S 2,3,4,5,6,11,15,33,49,50,52,53,54,57,60,61,64,68

%N Integers n such that A002110(n) + 2 is the sum of 2 nonzero squares.

%C Integers n such that A006862(n) + 1 is the sum of 2 nonzero squares.

%e a(1) = 2 because 2*3 + 2 = 2^2 + 2^2.

%e a(2) = 3 because 2*3*5 + 2 = 4^2 + 4^2.

%e a(3) = 4 because 2*3*5*7 + 2 = 14^2 + 4^2.

%t Rest@ Select[Range@ 36, SquaresR[2, Product[Prime@ k, {k, #}] + 2] > 0 &] (* _Michael De Vlieger_, Nov 23 2015 *)

%o (PARI) a(n) = prod(k=1, n, prime(k)) + 2;

%o is(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }

%o for(n=1, 1e5, if(is(a(n)), print1(n, ", ")))

%Y Cf. A000404, A002110, A006862.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Nov 20 2015