%I #33 Sep 20 2020 00:49:23

%S 9,25,121,361,841,3481,3721,5041,6241,10201,17161,19321,32761,39601,

%T 73441,121801,143641,167281,201601,212521,271441,323761,326041,398161,

%U 410881,436921,546121,564001,674041,776161,863041,982081,1062961,1079521,1104601,1142761,1190281,1274641,1324801

%N Square numbers in A070552.

%C All terms are == 1 (mod 8). For n > 2, a(n) == 1 (mod 120).

%C This sequence is a subsequence of A247687 and it contains the squares of all those primes p for which the areas of the 3 regions in the symmetric representation of p^2 (p once and (p^2 + 1)/2 twice), are primes; i.e., p^2 and p^2 + 1 are semiprimes (see A070552). The sequence of those primes p is A048161. Cf. A237593. - _Hartmut F. W. Hoft_, Aug 06 2020

%H Seiichi Manyama, <a href="/A263951/b263951.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A048161(n)^2.

%F From _Hartmut F. W. Hoft_, Aug 06 2020: (Start)

%F a(n) = 2 * A067755(n) + 1, n >= 1.

%F a(n+2) = 120 * A068485(n) + 1, n >= 1. (End)

%t a263951[n_] := Select[Map[Prime[#]^2&, Range[n]], PrimeQ[(#+1)/2]&]

%t a263951[190] (* _Hartmut F. W. Hoft_, Aug 06 2020 *)

%o (PARI) forprime(p=3, 2000, if(isprime((p^2+1)/2), print1(p^2, ", "))) \\ _Altug Alkan_, Oct 30 2015

%Y Subsequence of A070552.

%Y Cf. A048161, A067755, A068485, A237593, A247687, A263990.

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 30 2015