A275014 Upper ends of record gaps between numbers that are either primes or semiprimes.

3, 9, 29, 101, 247, 2531, 16033, 26615, 39359, 104677, 248426, 506531, 584237, 2560202, 4036993, 4417843, 5167619, 9725141, 25045807, 27489719, 70416301, 111555415, 174266734, 359589619, 1075714987, 6820213399, 15378035231, 16598109538, 19423306117, 30133946758, 74466436127

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) = A275013(n) + A275108(n).

Example

a(5) = 247 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(n", ")); 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(3); 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[2]); t=checkrange(t[2], q, r=t[2]-t[1])); p=q) \\ Charles R Greathouse IV, Nov 12 2016

Crossrefs

Cf. A037143, A111087, A275013, A275108.

Sequence in context: A148940 A169781 A162998 * A278404 A148941 A079319

Adjacent sequences: A275011 A275012 A275013 * A275015 A275016 A275017

Keyword

nonn

Author

Bobby Jacobs, Nov 12 2016

Extensions

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

Status

approved