A300898 Primes p such that p# + 4 is divisible by the next prime after p.
2, 3, 11, 107
Offset: 1
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The prime 11 is included because 2*3*5*7-1 is divisible by 11. Therefore, the last factor of the product, namely 7, is in A341812.
t=1;forprime(p=2,,((t-1)%p==0)&&print1(p,", ");t*=p)
The prime 7 is a member of this sequence because 2*3*5*7-1=209 is divisible by 11, the next prime immediately following 7. 11 is NOT a member of this sequence because 2*3*5*7*11-1=2309 is not divisible by 13 (leaves a remainder of 8), the next prime after 11.
isok(p) = if (isprime(p), my(a=Mod(1,nextprime(1+p))); forprime(q=2,p,a*=q); (a == 1)); \\ Michel Marcus, Mar 03 2021
7 belongs to this sequence since 2*3*5*7+11 is divisible by 13.
{ isgood(p) = local(r,p2,p3); p2=nextprime(p+1); p3=nextprime(p2+1); r=Mod(1,p3); forprime(q=1,p,r*=q); r+=p2; return(r==0); }
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