A263951 Square numbers in A070552.

9, 25, 121, 361, 841, 3481, 3721, 5041, 6241, 10201, 17161, 19321, 32761, 39601, 73441, 121801, 143641, 167281, 201601, 212521, 271441, 323761, 326041, 398161, 410881, 436921, 546121, 564001, 674041, 776161, 863041, 982081, 1062961, 1079521, 1104601, 1142761, 1190281, 1274641, 1324801

Offset: 1

Author

Zak Seidov, Oct 30 2015

Keywords

• nonn

Comments

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

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A070552.

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

Programs

Mathematica

a263951[n_] := Select[Map[Prime[#]^2&, Range[n]], PrimeQ[(#+1)/2]&]
a263951[190] (* Hartmut F. W. Hoft, Aug 06 2020 *)

PARI

forprime(p=3, 2000, if(isprime((p^2+1)/2), print1(p^2, ", "))) \\ Altug Alkan, Oct 30 2015

Formula

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

From Hartmut F. W. Hoft, Aug 06 2020: (Start)

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

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