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
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 30 2015
STATUS
approved