A097445 Second occurrence where n# - p is prime for primes p = 3, 5, ...

19, 197, 2293, 30011, 510463, 9699653, 223092809, 6469693163, 200560490051, 7420738134703, 304250263527157, 13082761331669881, 614889782588491313, 32589158477190044641, 1922760350154212638961, 117288381359406970983047

Offset

2,1

Comments

Care has to be taken to start with a large enough n to be sure terms are not missed. This was for n=100. This and A097444 were difficult to obtain using PARI.

Links

Table of n, a(n) for n=2..17.

Formula

n# is n primorial = product of primes 2*3*5*...*p <= n.

Example

3# = 2*3 = 6. 6 - 3 = 3 (first prime), 6 - 5 = 1, not prime, thus 3# - p is omitted.
5# = 2*3*5 = 30. 30 - 7 = 23 (first prime), 30 - 11 = 19 (second prime).

Prog

(PARI) primorm2(n) = { pr=1; for(x=1, n, f=1; pr*=prime(x); for(m=1, n, y=pr-prime(m); if(isprime(y), f=1; for(m=m+1, n, y=pr-prime(m); if(isprime(y), print1(y", "); f=0; break, f=1)); ); if(f==0, break) ) ) }

Crossrefs

Sequence in context: A048556 A141995 A210339 * A238697 A256639 A058370

Adjacent sequences: A097442 A097443 A097444 * A097446 A097447 A097448

Keyword

nonn

Author

Cino Hilliard, Aug 23 2004

Status

approved