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

1,1

Comments

Intersection of A000290 and A105571.

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000290, A001358, A105571.

Sequence in context: A173420 A271736 A280886 * A333007 A016862 A223506

Adjacent sequences: A278019 A278020 A278021 * A278023 A278024 A278025

Keyword

nonn

Author

K. D. Bajpai, Nov 08 2016

Status

approved