A059862 a(n) = Product_{i=3..n} (prime(i) - 3).
1, 1, 2, 8, 64, 640, 8960, 143360, 2867200, 74547200, 2087321600, 70968934400, 2696819507200, 107872780288000, 4746402332672000, 237320116633600000, 13289926531481600000, 770815738825932800000, 49332207284859699200000, 3354590095370459545600000, 234821306675932168192000000
Offset: 1
Keywords
Examples
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]
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.
Crossrefs
Programs
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Maple
a:= proc(n) option remember; `if`(n<3, 1, a(n-1)*(ithprime(n)-3)) end: seq(a(n), n=1..21); # Alois P. Heinz, Nov 19 2021 -
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 *) -
PARI
a(n) = prod(i=3, n, prime(i) - 3); \\ Michel Marcus, Jul 15 2018
Formula
a(1) = a(2) = 1; a(n) = a(n-1) * (prime(n) - 3) for n >= 3. - David A. Corneth, Jul 15 2018
Extensions
Name clarified, offset corrected by David A. Corneth, Jul 15 2018