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

1,1

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

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)

Mathematica

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

Prog

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

Crossrefs

Subsequence of A070552.

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

Sequence in context: A084058 A108570 A092769 * A139818 A227078 A146365

Adjacent sequences: A263948 A263949 A263950 * A263952 A263953 A263954

Keyword

nonn

Author

Zak Seidov, Oct 30 2015

Status

approved