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Chen semiprimes: semiprimes m such that m+4 is either a prime or a semiprime.
4

%I #7 Apr 15 2021 01:18:33

%S 6,9,10,15,21,22,25,33,34,35,39,49,51,55,57,58,65,69,82,85,87,91,93,

%T 111,115,118,119,123,129,133,141,142,145,155,159,169,177,183,187,201,

%U 202,205,209,213,214,215,217,219,235,237,247,249,253,259,265,267,274,287

%N Chen semiprimes: semiprimes m such that m+4 is either a prime or a semiprime.

%o (Python)

%o from sympy.ntheory.factor_ import primeomega, isprime

%o def issemiprime(n): return primeomega(n) == 2

%o def ok(n): return issemiprime(n) and (issemiprime(n+4) or isprime(n+4))

%o print(list(filter(ok, range(1, 288)))) # _Michael S. Branicky_, Apr 14 2021

%Y Cf. A109611, A175612.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 01 2010

%E Corrected (86 replaced by 85) by _R. J. Mathar_, Aug 03 2010