A275013 Lower ends of record gaps between numbers that are either primes or semiprimes.

2, 7, 26, 97, 241, 2521, 16022, 26603, 39343, 104659, 248407, 506509, 584213, 2560177, 4036967, 4417813, 5167587, 9725107, 25045771, 27489679, 70416259, 111555371, 174266683, 359589563, 1075714923, 6820213333, 15378035161, 16598109467, 19423306039, 30133946677, 74466436042

Offset

1,1

Comments

This sequence is infinite, since the asymptotic density of the primes and semiprimes is 0. - Charles R Greathouse IV, Nov 12 2016

Links

Giovanni Resta, Table of n, a(n) for n = 1..37 (terms < 10^13)

Formula

a(n) = A275014(n) - A275108(n).

Example

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

Prog

(PARI) r=0; last=2; for(n=3, 1e9, if(bigomega(n)<3, if(n-last>r, r=n-last; print1(last", ")); last=n)) \\ Charles R Greathouse IV, Nov 12 2016
(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(2); p=5; r=1; forprime(q=7, 1e9, if(q-p<=r, p=q; next); t=checkrange(p, q, r); while(t!=0, print1(", "t[1]); t=checkrange(t[2], q, r=t[2]-t[1])); p=q) \\ Charles R Greathouse IV, Nov 12 2016

Crossrefs

Cf. A037143, A111087, A275014, A275108.

Sequence in context: A129273 A055988 A371798 * A278351 A001075 A293210

Adjacent sequences: A275010 A275011 A275012 * A275014 A275015 A275016

Keyword

nonn

Author

Bobby Jacobs, Nov 12 2016

Extensions

a(7)-a(31) from Charles R Greathouse IV, Nov 12 2016

Status

approved