A058020 Difference between lcm(1,..,n) and the smallest prime > lcm(1,...,n) + 1, where n runs over A000961, lcm(n) runs through A051451.

3, 5, 5, 7, 11, 13, 11, 13, 31, 23, 19, 37, 41, 29, 31, 43, 53, 41, 53, 79, 59, 97, 59, 61, 113, 97, 179, 73, 73, 97, 103, 101, 109, 101, 229, 109, 139, 113, 227, 131, 191, 163, 139, 199, 151, 139, 181, 223, 229, 367, 239, 499, 251, 509, 251, 227, 373, 281, 233

Offset: 1

Author

Labos Elemer, Nov 14 2000

Keywords

• nonn

Comments

Analogous to Fortunate numbers and like them so far proved to be primes. This holds for x<=421: if Q is the first follower prime, then Q(421)-lcm(1,...421) = 557. For first some cases when 1+LCM is also a prime, the 2nd primes give 3,5,5,7,11,11,.. deviations, i.e. give primes.

Crossrefs

Cf. A000961, A003418, A051451, A057019, A037153, A035346, A005235, A054272, A055211, A037155, A045493, A038710 etc

Programs

PARI

N=1; for(n=2,1e3, if(isprimepower(n,&p), N*=p; print1(nextprime(N+2)-N", "))) \\ Charles R Greathouse IV, Nov 18 2015

Extensions

Name corrected by Charles R Greathouse IV, Nov 18 2015