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A263951 Square numbers in A070552. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 20 08:51 EDT 2021. Contains 347579 sequences. (Running on oeis4.)