# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a263951 Showing 1-1 of 1 %I A263951 #33 Sep 20 2020 00:49:23 %S A263951 9,25,121,361,841,3481,3721,5041,6241,10201,17161,19321,32761,39601, %T A263951 73441,121801,143641,167281,201601,212521,271441,323761,326041,398161, %U A263951 410881,436921,546121,564001,674041,776161,863041,982081,1062961,1079521,1104601,1142761,1190281,1274641,1324801 %N A263951 Square numbers in A070552. %C A263951 All terms are == 1 (mod 8). For n > 2, a(n) == 1 (mod 120). %C A263951 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 A263951 Seiichi Manyama, Table of n, a(n) for n = 1..10000 %F A263951 a(n) = A048161(n)^2. %F A263951 From _Hartmut F. W. Hoft_, Aug 06 2020: (Start) %F A263951 a(n) = 2 * A067755(n) + 1, n >= 1. %F A263951 a(n+2) = 120 * A068485(n) + 1, n >= 1. (End) %t A263951 a263951[n_] := Select[Map[Prime[#]^2&, Range[n]], PrimeQ[(#+1)/2]&] %t A263951 a263951[190] (* _Hartmut F. W. Hoft_, Aug 06 2020 *) %o A263951 (PARI) forprime(p=3, 2000, if(isprime((p^2+1)/2), print1(p^2, ", "))) \\ _Altug Alkan_, Oct 30 2015 %Y A263951 Subsequence of A070552. %Y A263951 Cf. A048161, A067755, A068485, A237593, A247687, A263990. %K A263951 nonn %O A263951 1,1 %A A263951 _Zak Seidov_, Oct 30 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE