

A275108


Record gaps between numbers that are either primes or semiprimes.


4



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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..37.


FORMULA

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


EXAMPLE

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


PROG

(PARI) checkrange(a, b, r)=while(ba>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(qp<=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


CROSSREFS

Cf. A037143, A111087, A275013, A275014.
Sequence in context: A047417 A066936 A067027 * A005457 A005453 A180242
Adjacent sequences: A275105 A275106 A275107 * A275109 A275110 A275111


KEYWORD

nonn,more


AUTHOR

Bobby Jacobs, Nov 13 2016


EXTENSIONS

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


STATUS

approved



