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The only semiprime s such that 2*a < s < 2*b where a, b are consecutive semiprimes.
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%I #20 Mar 18 2014 00:15:31

%S 51,69,74,77,106,111,115,129,187,226,235,237,267,291,314,355,371,403,

%T 407,411,422,427,437,497,519,533,591,597,649,655,669,713,723,763,785,

%U 789,831,893,905,939,943,965,1003,1027,1037,1059,1067,1073,1126,1159,1165

%N The only semiprime s such that 2*a < s < 2*b where a, b are consecutive semiprimes.

%H Alois P. Heinz, <a href="/A225801/b225801.txt">Table of n, a(n) for n = 1..1000</a>

%e 74 is the only semiprime in the interval [2*35, 2*38} = [70, 76] where 35, 38 are consecutive semiprimes.

%o (PARI) issemi(n)=bigomega(n)==2

%o precsemi(n)=while(!issemi(n--),); n

%o nextsemi(n)=while(!issemi(n++),); n

%o is(n)=if(!issemi(n),return(0)); my(a=precsemi(ceil(n/2)),b=nextsemi(n\2)); nextsemi(a)==b && nextsemi(2*a)==n && precsemi(2*b)==n \\ _Charles R Greathouse IV_, Mar 18 2014

%Y Cf. A001358, A166251, A217561.

%K nonn

%O 1,1

%A _Irina Gerasimova_, Aug 18 2013