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 A059862 a(n) = Product_{i=3..n} (prime(i) - 3). 3
 1, 1, 2, 8, 64, 640, 8960, 143360, 2867200, 74547200, 2087321600, 70968934400, 2696819507200, 107872780288000, 4746402332672000, 237320116633600000, 13289926531481600000, 770815738825932800000, 49332207284859699200000, 3354590095370459545600000, 234821306675932168192000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94. R. K. Guy, Unsolved Problems in Number Theory, A8, A1 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979. G. Polya, Mathematics and Plausible Reasoning, Vol. II, Appendix Princeton UP, 1954. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 C. K. Caldwell, Prime k-tuple Conjecture Steven R. Finch, Hardy-Littlewood Constants [Broken link] Steven R. Finch, Hardy-Littlewood Constants [From the Wayback machine] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes, Acta Mathematica, Vol. 44, pp. 1-70, 1923. G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy] G. Polya, Heuristic reasoning in the theory of numbers, Am. Math. Monthly, 66 (1959), 375-384. FORMULA a(1) = a(2) = 1, a(3) = 2; a(n + 1) = a(n) * (prime(n) - 3) for n >= 3. - David A. Corneth, Jul 15 2018 EXAMPLE For n = 6, a(6) = 640 because: prime(1..6)-3 = (-1,0,2,4,8,10) -> (1,1,2,4,8,10) and 1*1*2*4*8*10 = 640. [Example generalized and reformatted per observation of Jon E. Schoenfield by Harlan J. Brothers, Jul 15 2018] MATHEMATICA Join[{1, 1}, Table[Product[Prime[i] - 3, {i, 3, n}], {n, 3, 19}]] (* Harlan J. Brothers, Jul 02 2018 *) a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] (Prime[n] - 3); Table[a[n], {n, 19}] (* Harlan J. Brothers, Jul 02 2018 *) PROG (PARI) a(n) = prod(i=3, n, prime(i) - 3); \\ Michel Marcus, Jul 15 2018 CROSSREFS Cf. A049296, A002110, A005867, A000847, A022008, A051160-A051168, A048298, A059861-A059865. Sequence in context: A323853 A191570 A052707 * A268666 A193549 A005612 Adjacent sequences:  A059859 A059860 A059861 * A059863 A059864 A059865 KEYWORD nonn AUTHOR Labos Elemer, Feb 28 2001 EXTENSIONS Name clarified, offset corrected by David A. Corneth, Jul 15 2018 STATUS approved

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Last modified September 19 11:03 EDT 2019. Contains 327192 sequences. (Running on oeis4.)