

A067836


Let a(1)=2, f(n)=a(1)*a(2)*...*a(n1) for n>=1 and a(n)=nextprime(f(n)+1)f(n) for n>=2, where nextprime(x) is the smallest prime > x.


9



2, 3, 5, 7, 13, 11, 17, 19, 23, 37, 73, 29, 31, 43, 79, 53, 83, 67, 41, 47, 179, 149, 181, 103, 71, 59, 197, 167, 109, 137, 107, 251, 101, 157, 199, 283, 211, 277, 173, 127, 269, 61, 89, 271, 151, 191, 227, 311, 409, 577, 331, 281, 313, 307, 223, 491, 439, 233, 367
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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..n1} a(i) is prime.  Derek Orr, Jun 16 2015


LINKS

Robert Price and Dana Jacobsen, Table of n, a(n) for n = 1..3724 (first 1000 terms from Robert Price)
Frank Buss, Prime Puzzles  Frank Buss's Conjecture
Frank Buss, The B(n) function


MATHEMATICA

<<NumberTheory`PrimeQ` (* Load ProvablePrimeQ function, needed below. *)
f[1]=1; f[n_] := f[n]=f[n1]a[n1]; 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


CROSSREFS

Cf. A062894 has the indices of the primes in this sequence. A071290 has the sequence of f's. Also see A067362, A068192.
Sequence in context: A126056 A126055 A126054 * A332806 A108546 A065107
Adjacent sequences: A067833 A067834 A067835 * A067837 A067838 A067839


KEYWORD

nonn


AUTHOR

Frank Buss (fb(AT)frankbuss.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



