A278022 Squares s such that s + 2 and s - 2 are semiprime.

36, 121, 144, 289, 1764, 2304, 2601, 2809, 4225, 5184, 5329, 6241, 6889, 7056, 8100, 9409, 13225, 15625, 17689, 19881, 23409, 25281, 27225, 30276, 34969, 35721, 38025, 40401, 41616, 42849, 43681, 45369, 63001, 69696, 72361, 78961, 82369, 84681, 87025, 93636, 106929

Offset: 1

Author

K. D. Bajpai, Nov 08 2016

Keywords

• nonn

Comments

Intersection of A000290 and A105571.

Examples

			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.
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.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..5200

Crossrefs

Cf. A000290, A001358, A105571.

Programs

Mathematica

Select[Table[n^2, {n, 1000}], PrimeOmega[# + 2] == 2 &&  PrimeOmega[# - 2] == 2 &]
Select[Range[350]^2,PrimeOmega[#+{2,-2}]=={2,2}&] (* Harvey P. Dale, Jun 14 2021 *)

PARI

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