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 A111392 a(n) = Product_{i=1..n-1} (Product_{k=1..i} p_k + Product_{k=i+1..n} p_k). 5
 2, 5, 187, 162319, 10697595389, 63619487169453143, 74365399061678006800073593, 11864736003419293844093922527852416537, 601642845102734414280661105098046392912578705726003 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence gives another proof that there are infinitely many primes. Let N = Product_{1<=imul(mul(ithprime(k), k=1..i)+mul(ithprime(k), k=i+1..n), i=1..n-1): 2, seq(a(n), n=2..10); # Muniru A Asiru, Dec 06 2018 MATHEMATICA Join[{2}, Rest[f[n_]:=Product[(Product[Prime[k], {k, i}] + Product[Prime[k], {k, i + 1, n}]), {i, n - 1}]; Array[f, 10] ]] (* Robert G. Wilson v, Nov 12 2005 *) PROG (PARI) t=10; for(n=2, t, print1(prod(i=1, n-1, prod(k=1, i, prime(k)) + prod(k=i+1, n, prime(k))), ", ")); \\ Gerald McGarvey, Nov 12 2005 CROSSREFS Cf. A024451, A112404. Sequence in context: A116629 A124275 A013130 * A226071 A319143 A100366 Adjacent sequences: A111389 A111390 A111391 * A111393 A111394 A111395 KEYWORD nonn,nice AUTHOR Yasutoshi Kohmoto, Nov 08 2005 EXTENSIONS Corrected and extended by Gerald McGarvey and Robert G. Wilson v, Nov 12 2005 STATUS approved

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Last modified September 23 03:16 EDT 2023. Contains 365532 sequences. (Running on oeis4.)