A249241 - OEIS

%I #26 Dec 18 2017 02:59:48

%S 2,2,3,5,11,7,29,17,17,397,47,67,23,41,31,157,409,31,151,109,199,191,

%T 131,61,103,547,179,269,389,317,181,331,307,173,1259,1289,619,131,223,

%U 683,139,241,191,101,1039,1367,1153,241,1187,479,149,181,487,1093,571,1151,809,199,823,491,191,151,1321,197,163,337,467,659,673,877,487,743,313,673,857,677,1021

%N a(n) = p - prime(n)!/prime(n)#, where p is the smallest prime number > prime(n)!/prime(n)#+1.

%C Conjecture: All terms are prime.

%C While Fortune's conjecture (A005235) uses products of primes, this sequence uses products of composite numbers (more exactly: of nonprimes, because 1 belongs to them). It looks like all multiples of prime(n)# (except some powers) lead to a sequence which contains only prime numbers.

%e n = 1; prime(1)!/prime(1)# = 2/2 = 1; p = nextprime(1+1) = 3; a(1) = 3-1 = 2.

%o (MuPAD) q:=1; p:=1; for i from 1 to 100 do q:=nextprime(q+1); p:=p*q; N:=nextprime((fact(q)/p)+2)-fact(q)/p; print(i,N); end_for:

%o (PARI) A092435(n)=prime(n)!/prod(i=1,n,prime(i))

%o a(n)=my(t=A092435(n)); nextprime(t+2)-t \\ _Charles R Greathouse IV_, Oct 23 2014

%Y Cf. A092435.

%K nonn

%O 1,1

%A _Werner D. Sand_, Oct 23 2014