A283268 Smallest b-a such that a < prime(n)^2 < b, where a,b are semiprimes.
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, 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, 11, 11, 14, 15, 24, 10, 7, 12, 3, 7, 5, 12, 18, 3, 6, 4, 7, 12, 4
Offset: 2
Keywords
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 2..10000
Crossrefs
Cf. A283267.
Programs
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Mathematica
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 *) -
PARI
issemi(n)=bigomega(n)==2 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
Extensions
More terms from Peter J. C. Moses, Mar 04 2017
Comments