A068192 - OEIS

%I #12 Aug 01 2020 15:46:16

%S 2,3,5,7,11,13,17,19,31,29,23,41,43,37,89,59,53,67,79,71,137,109,239,

%T 167,199,47,83,97,61,373,101,179,193,131,151,73,263,593,139,113,157,

%U 103,241,181,397,233,617,311,191,229,271,269,127,223,331,337,211,163

%N Let a(1)=2, f(n) = 4*a(1)*a(2)*...*a(n-1) for n >= 1 and a(n) = f(n)-prevprime(f(n)-1) for n >= 2, where prevprime(x) is the largest prime < x.

%C The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?

%C First 1000 terms are primes. - _Mauro Fiorentini_, Aug 01 2020

%H Mauro Fiorentini, <a href="/A068192/b068192.txt">Table of n, a(n) for n = 1..1000</a>

%t <<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)

%t f[1]=4; f[n_] := f[n]=f[n-1]a[n-1]; a[n_] := a[n]=Module[{i}, For[i=2, True, i++, If[ProvablePrimeQ[f[n]-i], Return[i]]]]

%o (MuPAD) f := 4:for n from 1 to 50 do a := f-numlib::prevprime(f-2):f := f*a:print(a) end_for

%Y Cf. A068193 has the indices of the primes in this sequence. A066631 has the sequence of f's. Also see A067836.

%K nonn

%O 1,1

%A Frank Buss (fb(AT)frank-buss.de), Feb 19 2002

%E Edited by _Dean Hickerson_, Jun 10 2002