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A014545
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Primorial plus 1 prime indices: n such that n-th Euclid number A006862(n) = 1 + (Product of first n primes) is prime.
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43
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0, 1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, 1613, 2122, 2647, 2673, 4413, 13494, 31260, 33237
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OFFSET
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1,3
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COMMENTS
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The prime referenced by the final term of the sequence above (a(23) = 33237) has 169966 digits. - Harvey P. Dale, May 04 2012
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A005234 (values of p such that 1 + product of primes <= p is prime).
Cf. A018239 (primorial plus 1 primes).
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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EXTENSIONS
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a(21) from Arlin Anderson (starship1(AT)gmail.com), Oct 20 2000
Offset and first term changed by Altug Alkan, Nov 27 2015
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STATUS
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approved
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