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A060881
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n-th primorial (A002110) + prime(n + 1).
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4
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3, 5, 11, 37, 221, 2323, 30047, 510529, 9699713, 223092899, 6469693261, 200560490167, 7420738134851, 304250263527253, 13082761331670077, 614889782588491463, 32589158477190044789, 1922760350154212639131
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text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Terms are pairwise coprime with very high probability. I didn't find terms which are pairwise noncoprime, although it may be a case of the "strong law of small numbers." - Daniel Forgues, Apr 23 2012
All numbers in the range [primorial(n)+2, a(n)-1] are guaranteed to be a multiple of a prime p whose index is <= n. There are prime(n+1)-2 = A040976(n+1) such numbers. - Jamie Morken and Michel Marcus, Feb 01 2018
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 2*3 + 5 = 11.
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MAPLE
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a:= n-> mul(ithprime(k), k=1..n)+ithprime(n+1): seq(a(n), n=0..20); # Muniru A Asiru, Feb 01 2018
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MATHEMATICA
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Module[{nn=20, pr}, pr=Prime[Range[nn+1]]; Join[{3}, FoldList[ Times, Most[ pr]] + Rest[pr]]] (* Harvey P. Dale, Feb 19 2016 *)
Total /@ Fold[Append[#1, {Prime[#2] #1[[-1, 1]], Prime[#2 + 1]}] &, {{1, 2}}, Range@ 17] (* Michael De Vlieger, Feb 21 2018 *)
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PROG
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(PARI) { n=-1; m=1; forprime (p=2, prime(101), write("b060881.txt", n++, " ", m + p); m*=p; ) } \\ Harry J. Smith, Jul 19 2009
(PARI) a(n) = prod(i=1, n, prime(i)) + prime(n+1); \\ Michel Marcus, Feb 01 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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