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A059862 a(n) = Product_{i=3..n} (prime(i) - 3).

%I A059862 #44 Apr 03 2023 10:36:10
%S A059862 1,1,2,8,64,640,8960,143360,2867200,74547200,2087321600,70968934400,
%T A059862 2696819507200,107872780288000,4746402332672000,237320116633600000,
%U A059862 13289926531481600000,770815738825932800000,49332207284859699200000,3354590095370459545600000,234821306675932168192000000
%N A059862 a(n) = Product_{i=3..n} (prime(i) - 3).
%D A059862 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.
%D A059862 R. K. Guy, Unsolved Problems in Number Theory, A8, A1
%D A059862 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979.
%D A059862 G. Polya, Mathematics and Plausible Reasoning, Vol. II, Appendix Princeton UP, 1954.
%H A059862 Vincenzo Librandi, <a href="/A059862/b059862.txt">Table of n, a(n) for n = 1..200</a>
%H A059862 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=PrimeKtupleConjecture">Prime k-tuple Conjecture</a>
%H A059862 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/hrdyltl/hrdyltl.html">Hardy-Littlewood Constants </a> [Broken link]
%H A059862 Steven R. Finch, <a href="http://web.archive.org/web/20010614100031/http://www.mathsoft.com/asolve/constant/hrdyltl/hrdyltl.html">Hardy-Littlewood Constants </a> [From the Wayback machine]
%H A059862 G. H. Hardy and J. E. Littlewood, <a href="https://dx.doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes</a>, Acta Mathematica, Vol. 44, pp. 1-70, 1923.
%H A059862 G. Niklasch, <a href="/A001692/a001692.html">Some number theoretical constants: 1000-digit values</a> [Cached copy]
%H A059862 G. Polya, <a href="http://www.jstor.org/stable/2308748">Heuristic reasoning in the theory of numbers</a>, Am. Math. Monthly, 66 (1959), 375-384.
%F A059862 a(1) = a(2) = 1; a(n) = a(n-1) * (prime(n) - 3) for n >= 3. - _David A. Corneth_, Jul 15 2018
%e A059862 For n = 6, a(6) = 640 because:
%e A059862 prime(1..6)-3 = (-1,0,2,4,8,10) -> (1,1,2,4,8,10)
%e A059862 and
%e A059862 1*1*2*4*8*10 = 640. [Example generalized and reformatted per observation of _Jon E. Schoenfield_ by _Harlan J. Brothers_, Jul 15 2018]
%p A059862 a:= proc(n) option remember;
%p A059862       `if`(n<3, 1, a(n-1)*(ithprime(n)-3))
%p A059862     end:
%p A059862 seq(a(n), n=1..21);  # _Alois P. Heinz_, Nov 19 2021
%t A059862 Join[{1, 1}, Table[Product[Prime[i] - 3, {i, 3, n}], {n, 3, 19}]] (* _Harlan J. Brothers_, Jul 02 2018 *)
%t A059862 a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] (Prime[n] - 3);
%t A059862 Table[a[n], {n, 19}] (* _Harlan J. Brothers_, Jul 02 2018 *)
%o A059862 (PARI) a(n) = prod(i=3, n, prime(i) - 3); \\ _Michel Marcus_, Jul 15 2018
%Y A059862 Cf. A049296, A002110, A005867, A000847, A022008, A051160-A051168, A048298, A059861-A059865.
%K A059862 nonn
%O A059862 1,3
%A A059862 _Labos Elemer_, Feb 28 2001
%E A059862 Name clarified, offset corrected by _David A. Corneth_, Jul 15 2018