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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.)