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

3, 7, 176078267

Offset

1,1

Comments

Here p# means A034386(p).

The next prime after p is then in A341804.

Links

Table of n, a(n) for n=1..3.

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

Example

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.

Prog

(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

Crossrefs

Cf. A057588, A058233, A341804, A341805.

Sequence in context: A351848 A137125 A103319 * A153021 A155979 A120669

Adjacent sequences: A341809 A341810 A341811 * A341813 A341814 A341815

Keyword

nonn,bref,hard,more

Author

Jeppe Stig Nielsen, Feb 20 2021

Status

approved