A275108 Record gaps between numbers that are either primes or semiprimes.

1, 2, 3, 4, 6, 10, 11, 12, 16, 18, 19, 22, 24, 25, 26, 30, 32, 34, 36, 40, 42, 44, 51, 56, 64, 66, 70, 71, 78, 81, 85, 86, 91, 106, 110, 112, 128

Offset: 1

Author

Bobby Jacobs, Nov 13 2016

Keywords

• nonn
• more

Examples

			a(5) = 6 because the next prime or semiprime after 241 is 247, and that is a record gap of size 6.
		

Crossrefs

Cf. A037143, A111087, A275013, A275014.

Programs

PARI

checkrange(a, b, r)=while(b-a>r, forstep(n=a+r, a+1, -1, if(bigomega(n)<3, a=n; next(2))); for(n=a+r+1, b, if(bigomega(n)<3, return([a, n])))); 0
print1(1); p=5; r=1; forprime(q=7, 1e9, if(q-p<=r, p=q; next); t=checkrange(p, q, r); while(t, print1(", "t[2]-t[1]); t=checkrange(t[2], q, r=t[2]-t[1])); p=q) \\ Charles R Greathouse IV, Nov 19 2016

Formula

a(n) = A275014(n) - A275013(n).

Extensions

a(32)-a(37) from Giovanni Resta, Apr 25 2020