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Squares s such that s + 2 and s - 2 are semiprime.
2

%I #9 Jun 14 2021 15:19:17

%S 36,121,144,289,1764,2304,2601,2809,4225,5184,5329,6241,6889,7056,

%T 8100,9409,13225,15625,17689,19881,23409,25281,27225,30276,34969,

%U 35721,38025,40401,41616,42849,43681,45369,63001,69696,72361,78961,82369,84681,87025,93636,106929

%N Squares s such that s + 2 and s - 2 are semiprime.

%C Intersection of A000290 and A105571.

%H K. D. Bajpai, <a href="/A278022/b278022.txt">Table of n, a(n) for n = 1..5200</a>

%e a(1) = 36 appears in the list because 36 = 6^2 (square) and 36 + 2 = 38 = 19*2; 36 - 2 = 34 = 17*2; both are semiprime.

%e a(2) = 121 appears in the list because 121 = 11^2 (square) and 121 + 2 = 123 = 41*3;121 - 2 = 119 = 17*7; both are semiprime.

%t Select[Table[n^2, {n, 1000}], PrimeOmega[# + 2] == 2 && PrimeOmega[# - 2] == 2 &]

%t Select[Range[350]^2,PrimeOmega[#+{2,-2}]=={2,2}&] (* _Harvey P. Dale_, Jun 14 2021 *)

%o (PARI) for(n = 1, 1000, s = n^2; if( bigomega(s+2)==2 && bigomega(s-2)==2, print1(s, ", ")))

%Y Cf. A000290, A001358, A105571.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Nov 08 2016