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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. 39
 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. 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[180]]]]+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 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 A229347 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 December 12 13:48 EST 2018. Contains 318063 sequences. (Running on oeis4.)