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 A014545 Primorial plus 1 prime indices: n such that n-th Euclid number A006862(n) = 1 + (Product of first n primes) is prime. 40
 0, 1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, 1613, 2122, 2647, 2673, 4413, 13494, 31260, 33237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The prime referenced by the final term of the sequence above (a(23) = 33237) has 169966 digits. - Harvey P. Dale, May 04 2012 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008. LINKS C. K. Caldwell, Prime Pages: Database Search C. K. Caldwell, Primorial Primes H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183. Benny Lim, Prime Numbers Generated From Highly Composite Numbers, Parabola (2018) Vol. 54, Issue 3. Eric Weisstein's World of Mathematics, Euclid Number Eric Weisstein's World of Mathematics, Primorial Prime Eric Weisstein's World of Mathematics, Integer Sequence Primes FORMULA a(n+1) = A000720(A005234(n)). - M. F. Hasler, May 31 2018 EXAMPLE a(1) = 0 because the (empty) product of 0 primes is 1, plus 1 yields the prime 2. prime(4413) = 42209 and Primorial(4413) + 1 = 42209# + 1 is a 18241-digit prime. prime(13494) = 145823 and Primorial(13494) + 1 = 145823# + 1 is a 63142-digit prime. MAPLE P:= 1: p:= 1: count:= 0: for n from 1 to 1000 do   p:= nextprime(p);   P:= P*p;   if isprime(P+1) then     count:= count+1;     A[count]:= n;   fi od: seq(A[i], i=1..count); # Robert Israel, Nov 04 2015 MATHEMATICA Flatten[Position[Rest[FoldList[Times, 1, Prime[Range]]]+1, _?PrimeQ]] (* Harvey P. Dale, May 04 2012 *) (* this program generates the first 9 positive terms of the sequence; changing the Range constant to 33237 will generate all 23 terms above, but it will take a long time to do so *) PROG (PARI) is(n)=ispseudoprime(prod(i=1, n, prime(i))+1) \\ Charles R Greathouse IV, Mar 21 2013 (PARI) P=1; n=0; forprime(p=1, 10^5, if(ispseudoprime(P+1), print1(n", ")); n=n+1; P*=p; ) \\ Hans Loeblich, May 10 2019 CROSSREFS Cf. A005234 (values of p such that 1 + product of primes <= p is prime). Cf. A018239 (primorial plus 1 primes). Cf. A002110, A006862, A057704. Sequence in context: A280206 A190783 A136367 * A158930 A065636 A328260 Adjacent sequences:  A014542 A014543 A014544 * A014546 A014547 A014548 KEYWORD nonn,nice,hard,more AUTHOR EXTENSIONS More terms from Labos Elemer a(21) from Arlin Anderson (starship1(AT)gmail.com), Oct 20 2000 a(22)-a(23) from Eric W. Weisstein, Mar 13 2004 (based on information in A057704) Offset and first term changed by Altug Alkan, Nov 27 2015 STATUS approved

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Last modified October 20 02:18 EDT 2019. Contains 328244 sequences. (Running on oeis4.)