A341812 Primes p such that p#-1 is divisible by the next prime after p.

3, 7, 176078267

Offset: 1

Author

Jeppe Stig Nielsen, Feb 20 2021

Keywords

• nonn
• bref
• hard
• more

Comments

Here p# means A034386(p).

The next prime after p is then in A341804.

Examples

			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.
		

Links

• Carlos Rivera, Puzzle 117. Certain p#+1 values, contains message from Wilfred Whiteside mentioning this sequence.

Crossrefs

Cf. A057588, A058233, A341804, A341805.

Programs

PARI

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