OFFSET
1,1
COMMENTS
The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?
All elements are prime and distinct through n=1000. - Robert Price, Mar 09 2013
All elements are prime and distinct through n=3724. - Dana Jacobsen, Feb 15 2015
With a(0) = 1, a(n) is the next smallest number not in the sequence such that a(n) + Product_{i=1..n-1} a(i) is prime. - Derek Orr, Jun 16 2015
A generalization of Fortunate's conjecture, cf. A005235. - M. F. Hasler, Nov 04 2024
LINKS
Robert Price and Dana Jacobsen, Table of n, a(n) for n = 1..3724 (first 1000 terms from Robert Price)
Carlos Rivera, Prime Puzzles - Conjecture 28. Frank Buss's Conjecture
Carlos Rivera, Conjecture 29. The Frank Buss's B(n) function
MATHEMATICA
<<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)
f[1]=1; 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]]]]
Join[{a = 2}, f = 1; Table[f = f*a; a = NextPrime[f + 1] - f; a, {n, 2, 59}]] (* Jayanta Basu, Aug 10 2013 *)
PROG
(MuPAD) f := 1:for n from 1 to 50 do a := nextprime(f+2)-f:f := f*a:print(a) end_for
(PARI) v=[2]; n=2; while(n<500, s=n+prod(i=1, #v, v[i]); if(isprime(s)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=1); n++); v \\ Derek Orr, Jun 16 2015
(Python)
from sympy import nextprime
def A067836_gen(): # generator of terms
a, f = 2, 1
yield 2
while True:
yield (a:=nextprime((f:=f*a)+1)-f)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Frank Buss (fb(AT)frank-buss.de), Feb 09 2002
EXTENSIONS
Edited by Dean Hickerson, Mar 02 2002
Edited by Dean Hickerson and David W. Wilson, Jun 10 2002
STATUS
approved