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%I #15 Mar 06 2017 03:22:18
%S 4,4,5,3,11,4,4,6,4,6,5,6,8,9,4,9,7,10,9,4,3,4,19,4,4,11,12,6,6,15,9,
%T 8,7,6,6,7,12,12,10,14,7,12,14,6,3,9,10,7,8,5,9,6,4,7,5,4,13,8,4,14,
%U 11,11,14,15,24,10,7,12,3,7,5,12,18,3,6,4,7,12,4
%N Smallest b-a such that a < prime(n)^2 < b, where a,b are semiprimes.
%C This is the second sequence of the series of ones defined in A283267.
%H Charles R Greathouse IV, <a href="/A283268/b283268.txt">Table of n, a(n) for n = 2..10000</a>
%e a(2) = 4 since prime(2)^2 = 3^2 = 9; 6 < 9 < 10, 6 = 2*3 and 10 = 2*5; 10 - 6 = 4. The number prime(1)^2 = 2^2 = 4 is the smallest semiprime, therefore the offset of the sequence is 2 since there are no positive semiprimes less than 4.
%t Table[Module[{m = Prime[n]^2, a, b}, a = m - 1; b = m + 1; While[PrimeOmega@ a != 2, a--]; While[PrimeOmega@ b != 2, b++]; b - a], {n, 2, 120}] (* _Michael De Vlieger_, Mar 04 2017 *)
%o (PARI) issemi(n)=bigomega(n)==2
%o a(n, p=prime(n))=my(a=p^2, b=a); while(!issemi(a--), ); while(!issemi(b++), ); b-a \\ _Charles R Greathouse IV_, Mar 06 2017
%Y Cf. A283267.
%K nonn
%O 2,1
%A _Vladimir Shevelev_, Mar 04 2017
%E More terms from _Peter J. C. Moses_, Mar 04 2017
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