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 A089305 Smallest prime of the form n*(n+1)*(n+2)...(n+k) + 1, k > 0, i.e., a(n) > n+1, or 0 if no such prime exists. 0
 3, 7, 13, 604801, 31, 43, 55441, 73, 991, 1321, 670442572801, 157, 2731, 211, 241, 39070081, 307, 6841, 4037881, 421, 463, 173059286401, 725902806896876799590400001, 601, 17551, 530122321, 757, 24165121, 45143585625601, 29761, 5296855682339020801, 63606090241, 1123, 42841, 4758977059201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: No entry is zero. LINKS EXAMPLE a(1) = 1*2 + 1 = 3 and not 2. a(4) = 604801 = 4*5*6*7*8*9*10 + 1 and 4*5 + 1, 4*5*6 + 1, etc. up to 4*5*...*9 + 1 are composite. MAPLE for i from 2 while i < 40 do c := i; for j from i+1 while j < 10000000 do c := c*j; if (isprime(c+1)) then print(i, j, c+1); break; end if; end do; end do; # Jim Nastos MATHEMATICA sp[n_]:=Module[{k=1}, While[!PrimeQ[Times@@Range[n, n+k]+1], k++]; Times@@ Range[ n, n+k]+1]; Array[sp, 40] (* Harvey P. Dale, Jun 17 2014 *) CROSSREFS Cf. A087564. Sequence in context: A084741 A135623 A172291 * A112618 A058027 A128661 Adjacent sequences:  A089302 A089303 A089304 * A089306 A089307 A089308 KEYWORD nonn AUTHOR Amarnath Murthy, Nov 01 2003 EXTENSIONS More terms from Jim Nastos, Nov 02 2003 More terms from David Wasserman, Sep 09 2005 STATUS approved

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Last modified September 28 21:42 EDT 2020. Contains 337410 sequences. (Running on oeis4.)