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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. 36
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

Table of n, a(n) for n=1..23.

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

EXAMPLE

p(4413)=42209 and Primorial(4413)+1=42209#+1 is a 18241-digit prime. Also p(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: A032988 A190783 A136367 * A158930 A065636 A229347

Adjacent sequences:  A014542 A014543 A014544 * A014546 A014547 A014548

KEYWORD

nonn,nice,hard,more,changed

AUTHOR

Eric W. Weisstein, Murray R. Bremner

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 8 01:14 EST 2016. Contains 278902 sequences.