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

2,1

Comments

This is the second sequence of the series of ones defined in A283267.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A283267.

Sequence in context: A307983 A330305 A011333 * A016709 A023403 A091283

Adjacent sequences: A283265 A283266 A283267 * A283269 A283270 A283271

Keyword

nonn

Author

Vladimir Shevelev, Mar 04 2017

Extensions

More terms from Peter J. C. Moses, Mar 04 2017

Status

approved