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(n) = a(n-1) * (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]
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 *)
PROG
(PARI) a(n) = prod(i=3, n, prime(i) - 3); \\ Michel Marcus, Jul 15 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 28 2001
EXTENSIONS
Name clarified, offset corrected by David A. Corneth, Jul 15 2018
STATUS
approved