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Primes p such that p#-1 is divisible by the next prime after p.
2

%I #11 Mar 03 2021 22:05:18

%S 3,7,176078267

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

%C Here p# means A034386(p).

%C The next prime after p is then in A341804.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_117.htm">Puzzle 117. Certain p#+1 values</a>, contains message from Wilfred Whiteside mentioning this sequence.

%e 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.

%e 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.

%o (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

%Y Cf. A057588, A058233, A341804, A341805.

%K nonn,bref,hard,more

%O 1,1

%A _Jeppe Stig Nielsen_, Feb 20 2021